Publications
1.
Gottardini, Andrea; Cecchin, Leonardo; Demir, Ozan; Fagiano, Lorenzo
Data-Driven Nonlinear Model Predictive Control for Grading Functions for Excavators Working paper Forthcoming
Forthcoming.
@workingpaper{gottardini_data-driven_2025,
title = {Data-Driven Nonlinear Model Predictive Control for Grading Functions for Excavators},
author = {Andrea Gottardini and Leonardo Cecchin and Ozan Demir and Lorenzo Fagiano},
year = {2025},
date = {2025-12-31},
abstract = {Hydraulic excavators are essential construc-
tion machines widely utilized for ground shaping tasks,
such as horizontal leveling and creating sloped surfaces.
These operations require a high degree of precision, which
can be challenging for unskilled workers.
The implementation of automation in hydraulic machin-
ery has the potential to significantly enhance productivity
by improving accuracy and reducing reliance on highly
trained labor. However, the control of hydraulic systems is
complicated by strong nonlinearities and variability among
machines, making the design of effective controllers a sig-
nificant challenge.
In this paper, we propose a data-driven Model Predictive
Control (MPC) system, initially developed for trajectory
tracking and subsequently adapted for a path following
approach. This adaptation is crucial because the trajectory
tracking method relies on open-loop references, using a
predefined speed profile that does not account for the
dynamics of the hydraulic excavator, potentially leading to
difficult-to-follow trajectories.
The prediction model used in the MPC is based on Linear
Local Neuro-Fuzzy Models, trained with the LOcal LInear
MOdel Tree (LOLIMOT) algorithm, while the linear parame-
ters are refined using the Simulation Error Method (SEM).
The proposed control system was rigorously tested on
a JCB Hydradig 110W following a comprehensive data
collection campaign to obtain the necessary data for the
data-driven model of the hydraulic cylinders.
Results, evaluated using metrics such as root mean
square error (RMSE) between the actual and reference
paths, maximum error, and standard deviation (indicating
oscillations during motion), demonstrate that our approach
outperforms previous data-driven feed-forward controllers,
highlighting its efficacy in enhancing hydraulic automation.},
keywords = {},
pubstate = {forthcoming},
tppubtype = {workingpaper}
}
Hydraulic excavators are essential construc-
tion machines widely utilized for ground shaping tasks,
such as horizontal leveling and creating sloped surfaces.
These operations require a high degree of precision, which
can be challenging for unskilled workers.
The implementation of automation in hydraulic machin-
ery has the potential to significantly enhance productivity
by improving accuracy and reducing reliance on highly
trained labor. However, the control of hydraulic systems is
complicated by strong nonlinearities and variability among
machines, making the design of effective controllers a sig-
nificant challenge.
In this paper, we propose a data-driven Model Predictive
Control (MPC) system, initially developed for trajectory
tracking and subsequently adapted for a path following
approach. This adaptation is crucial because the trajectory
tracking method relies on open-loop references, using a
predefined speed profile that does not account for the
dynamics of the hydraulic excavator, potentially leading to
difficult-to-follow trajectories.
The prediction model used in the MPC is based on Linear
Local Neuro-Fuzzy Models, trained with the LOcal LInear
MOdel Tree (LOLIMOT) algorithm, while the linear parame-
ters are refined using the Simulation Error Method (SEM).
The proposed control system was rigorously tested on
a JCB Hydradig 110W following a comprehensive data
collection campaign to obtain the necessary data for the
data-driven model of the hydraulic cylinders.
Results, evaluated using metrics such as root mean
square error (RMSE) between the actual and reference
paths, maximum error, and standard deviation (indicating
oscillations during motion), demonstrate that our approach
outperforms previous data-driven feed-forward controllers,
highlighting its efficacy in enhancing hydraulic automation.
tion machines widely utilized for ground shaping tasks,
such as horizontal leveling and creating sloped surfaces.
These operations require a high degree of precision, which
can be challenging for unskilled workers.
The implementation of automation in hydraulic machin-
ery has the potential to significantly enhance productivity
by improving accuracy and reducing reliance on highly
trained labor. However, the control of hydraulic systems is
complicated by strong nonlinearities and variability among
machines, making the design of effective controllers a sig-
nificant challenge.
In this paper, we propose a data-driven Model Predictive
Control (MPC) system, initially developed for trajectory
tracking and subsequently adapted for a path following
approach. This adaptation is crucial because the trajectory
tracking method relies on open-loop references, using a
predefined speed profile that does not account for the
dynamics of the hydraulic excavator, potentially leading to
difficult-to-follow trajectories.
The prediction model used in the MPC is based on Linear
Local Neuro-Fuzzy Models, trained with the LOcal LInear
MOdel Tree (LOLIMOT) algorithm, while the linear parame-
ters are refined using the Simulation Error Method (SEM).
The proposed control system was rigorously tested on
a JCB Hydradig 110W following a comprehensive data
collection campaign to obtain the necessary data for the
data-driven model of the hydraulic cylinders.
Results, evaluated using metrics such as root mean
square error (RMSE) between the actual and reference
paths, maximum error, and standard deviation (indicating
oscillations during motion), demonstrate that our approach
outperforms previous data-driven feed-forward controllers,
highlighting its efficacy in enhancing hydraulic automation.
2.
Msaad, Salim; Cecchin, Leonardo; Demir, Ozan; Fagiano, Lorenzo
Data-Driven Model Predictive Control of an Hydraulic Excavator via Local Model Networks Proceedings Article Forthcoming
In: 2025 American Control Conference (ACC), Forthcoming.
@inproceedings{msaad_data-driven_2025,
title = {Data-Driven Model Predictive Control of an Hydraulic Excavator via Local Model Networks},
author = {Salim Msaad and Leonardo Cecchin and Ozan Demir and Lorenzo Fagiano},
year = {2025},
date = {2025-07-01},
urldate = {2025-07-01},
publisher = {2025 American Control Conference (ACC)},
abstract = {A novel solution to control an hydraulic excavator during grading tasks is proposed, featuring a Model Predictive Controller designed using Local Model Networks (LMNs), i.e. linear time-invariant dynamic models averaged by nonlinear static functions. The Local Linear Models Tree (LoLiMoT) algorithm is employed to derive an LMN from experimental data of a real excavator. Then, a nonlinear MPC law is designed and implemented on the excavator’s embedded control system. To further improve the computational efficiency, a time-varying MPC law is designed as well, where the LMN is linearized in real-time using the previously computed optimal trajectory. Experimental results, conducted with the excavator in realworld conditions, show the effectiveness of both approaches in achieving performance comparable to state-of-the-art solutions, while utilizing a more compact dataset and without the need of the hydraulic cylinders’ pressure measurement.},
keywords = {},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}
A novel solution to control an hydraulic excavator during grading tasks is proposed, featuring a Model Predictive Controller designed using Local Model Networks (LMNs), i.e. linear time-invariant dynamic models averaged by nonlinear static functions. The Local Linear Models Tree (LoLiMoT) algorithm is employed to derive an LMN from experimental data of a real excavator. Then, a nonlinear MPC law is designed and implemented on the excavator’s embedded control system. To further improve the computational efficiency, a time-varying MPC law is designed as well, where the LMN is linearized in real-time using the previously computed optimal trajectory. Experimental results, conducted with the excavator in realworld conditions, show the effectiveness of both approaches in achieving performance comparable to state-of-the-art solutions, while utilizing a more compact dataset and without the need of the hydraulic cylinders’ pressure measurement.
3.
Allamaa, Jean Pierre; Patrinos, Panagiotis; Son, Tong Duy
ExAMPC: the Data-Driven Explainable and Approximate NMPC with Physical Insights Working paper
2025, (Submitted for possible publication in IEEE).
@workingpaper{allamaa2025exampc,
title = {ExAMPC: the Data-Driven Explainable and Approximate NMPC with Physical Insights},
author = {Jean Pierre Allamaa and Panagiotis Patrinos and Tong Duy Son},
url = {https://arxiv.org/abs/2503.00654},
year = {2025},
date = {2025-06-18},
abstract = {Amidst the surge in the use of Artificial Intelligence (AI) for control purposes, classical and model-based control methods maintain their popularity due to their transparency and deterministic nature. However, advanced controllers like Nonlinear Model Predictive Control (NMPC), despite proven capabilities, face adoption challenges due to their computational complexity and unpredictable closed-loop performance in complex validation systems. This paper introduces ExAMPC, a methodology bridging classical control and explainable AI by augmenting the NMPC with data-driven insights to improve the trustworthiness and reveal the optimization solution and closed-loop performance's sensitivities to physical variables and system parameters. By employing a low-order spline embedding to reduce the open-loop trajectory dimensionality by over 95%, and integrating it with SHAP and Symbolic Regression from eXplainable AI (XAI) for an approximate NMPC, we enable intuitive physical insights into the NMPC's optimization routine. The prediction accuracy of the approximate NMPC is enhanced through physics-inspired continuous-time constraints penalties, reducing the predicted continuous trajectory violations by 93%. ExAMPC enables accurate forecasting of the NMPC's computational requirements with explainable insights on worst-case scenarios. Experimental validation on automated valet parking and autonomous racing with lap-time optimization NMPC, demonstrates the methodology's practical effectiveness in real-world applications.},
note = {Submitted for possible publication in IEEE},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Amidst the surge in the use of Artificial Intelligence (AI) for control purposes, classical and model-based control methods maintain their popularity due to their transparency and deterministic nature. However, advanced controllers like Nonlinear Model Predictive Control (NMPC), despite proven capabilities, face adoption challenges due to their computational complexity and unpredictable closed-loop performance in complex validation systems. This paper introduces ExAMPC, a methodology bridging classical control and explainable AI by augmenting the NMPC with data-driven insights to improve the trustworthiness and reveal the optimization solution and closed-loop performance's sensitivities to physical variables and system parameters. By employing a low-order spline embedding to reduce the open-loop trajectory dimensionality by over 95%, and integrating it with SHAP and Symbolic Regression from eXplainable AI (XAI) for an approximate NMPC, we enable intuitive physical insights into the NMPC's optimization routine. The prediction accuracy of the approximate NMPC is enhanced through physics-inspired continuous-time constraints penalties, reducing the predicted continuous trajectory violations by 93%. ExAMPC enables accurate forecasting of the NMPC's computational requirements with explainable insights on worst-case scenarios. Experimental validation on automated valet parking and autonomous racing with lap-time optimization NMPC, demonstrates the methodology's practical effectiveness in real-world applications.
4.
Lahr, Amon; Köhler, Johannes; Scampicchio, Anna; Zeilinger, Melanie N.
Optimal Kernel Regression Bounds under Energy-Bounded Noise Working paper
2025.
@workingpaper{lahr_optimal_2025,
title = {Optimal Kernel Regression Bounds under Energy-Bounded Noise},
author = {Amon Lahr and Johannes Köhler and Anna Scampicchio and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2505.22235},
year = {2025},
date = {2025-05-28},
abstract = {Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic uncertainty bound for kernel-based estimation, which can also handle correlated noise sequences. Its computation relies on a mild norm-boundedness assumption on the unknown function and the noise, returning the worst-case function realization within the hypothesis class at an arbitrary query input location. The value of this function is shown to be given in terms of the posterior mean and covariance of a Gaussian process for an optimal choice of the measurement noise covariance. By rigorously analyzing the proposed approach and comparing it with other results in the literature, we show its effectiveness in returning tight and easy-to-compute bounds for kernel-based estimates.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic uncertainty bound for kernel-based estimation, which can also handle correlated noise sequences. Its computation relies on a mild norm-boundedness assumption on the unknown function and the noise, returning the worst-case function realization within the hypothesis class at an arbitrary query input location. The value of this function is shown to be given in terms of the posterior mean and covariance of a Gaussian process for an optimal choice of the measurement noise covariance. By rigorously analyzing the proposed approach and comparing it with other results in the literature, we show its effectiveness in returning tight and easy-to-compute bounds for kernel-based estimates.
5.
Prajapat, Manish; Köhler, Johannes; Lahr, Amon; Krause, Andreas; Zeilinger, Melanie N.
Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics Working paper
2025.
@workingpaper{prajapat_finite_sample_based_2025,
title = {Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics},
author = {Manish Prajapat and Johannes Köhler and Amon Lahr and Andreas Krause and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2505.07594},
year = {2025},
date = {2025-05-12},
abstract = {Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safetyaware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC) methods either rely on approximations, thus lacking guarantees, or are overly conservative, which limits their practical utility. To close this gap, we present a sampling-based framework that efficiently propagates the model’s epistemic uncertainty while avoiding conservatism. We establish a novel sample complexity result that enables the construction of a reachable set using a finite number of dynamics functions sampled from the GP posterior. Building on this, we design a sampling-based GP-MPC scheme that is recursively feasible and guarantees closed-loop safety and stability with high probability. Finally, we showcase the effectiveness of our method on two numerical examples, highlighting accurate reachable set over-approximation and safe closed-loop performance.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Gaussian Process (GP) regression is shown to be effective for learning unknown dynamics, enabling efficient and safetyaware control strategies across diverse applications. However, existing GP-based model predictive control (GP-MPC) methods either rely on approximations, thus lacking guarantees, or are overly conservative, which limits their practical utility. To close this gap, we present a sampling-based framework that efficiently propagates the model’s epistemic uncertainty while avoiding conservatism. We establish a novel sample complexity result that enables the construction of a reachable set using a finite number of dynamics functions sampled from the GP posterior. Building on this, we design a sampling-based GP-MPC scheme that is recursively feasible and guarantees closed-loop safety and stability with high probability. Finally, we showcase the effectiveness of our method on two numerical examples, highlighting accurate reachable set over-approximation and safe closed-loop performance.
6.
Wang, Renzi; Schuurmans, Mathijs; Patrinos, Panagiotis
Risk-Sensitive Model Predictive Control for Interaction-Aware Planning--A Sequential Convexification Algorithm Working paper
2025.
@workingpaper{wang2025risk,
title = {Risk-Sensitive Model Predictive Control for Interaction-Aware Planning--A Sequential Convexification Algorithm},
author = {Renzi Wang and Mathijs Schuurmans and Panagiotis Patrinos},
url = {https://doi.org/10.48550/arXiv.2503.14328},
year = {2025},
date = {2025-03-18},
abstract = {This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable convex upper bounds to both the objective function, and to frequently used penalty terms for collision avoidance, allowing us to efficiently solve the generally nonconvex optimal control problem as a sequence of convex problems. Simulations of a robot navigating a corridor demonstrate the effectiveness and the computational advantage of the proposed approach.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable convex upper bounds to both the objective function, and to frequently used penalty terms for collision avoidance, allowing us to efficiently solve the generally nonconvex optimal control problem as a sequence of convex problems. Simulations of a robot navigating a corridor demonstrate the effectiveness and the computational advantage of the proposed approach.
7.
Yang, Shaohui; Ohtsuka, Toshiyuki; Jones, Colin
Brunovsky Riccati Recursion for Linear Model Predictive Control Proceedings Article Forthcoming
In: Forthcoming.
@inproceedings{yang2025brunovsky,
title = {Brunovsky Riccati Recursion for Linear Model Predictive Control},
author = {Shaohui Yang and Toshiyuki Ohtsuka and Colin Jones },
year = {2025},
date = {2025-02-14},
keywords = {},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}
8.
Yang, Shaohui; Ohtsuka, Toshiyuki; Plancher, Brian; Jones, Colin
Polynomial and Parallelizable Preconditioning of Linear Systems for Model Predictive Control and Beyond Working paper
2025.
@workingpaper{yang2025polynomial,
title = {Polynomial and Parallelizable Preconditioning of Linear Systems for Model Predictive Control and Beyond},
author = {Shaohui Yang and Toshiyuki Ohtsuka and Brian Plancher and Colin Jones},
year = {2025},
date = {2025-02-14},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
9.
Yang, Shaohui; Jones, Colin
Enhanced Numerical Techniques and Efficient Implementation for Brunovsky Form-Based Linear Model Predictive Control Working paper
2025.
@workingpaper{yang2025enhanced,
title = {Enhanced Numerical Techniques and Efficient Implementation for Brunovsky Form-Based Linear Model Predictive Control},
author = {Shaohui Yang and Colin Jones },
year = {2025},
date = {2025-02-14},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
10.
Scampicchio, Anna; Arcari, Elena; Lahr, Amon; Zeilinger, Melanie N.
Gaussian Processes for Dynamics Learning in Model Predictive Control Working paper
2025.
@workingpaper{scampicchio_gaussian_2025,
title = {Gaussian Processes for Dynamics Learning in Model Predictive Control},
author = {Anna Scampicchio and Elena Arcari and Amon Lahr and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2502.02310},
year = {2025},
date = {2025-02-04},
abstract = {Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies. This has enabled a plethora of successful implementations of Gaussian process-based model predictive control in a variety of applications over the last years. However, despite its evident practical effectiveness, there are still many open questions when attempting to analyze the associated optimal control problem theoretically and to exploit the full potential of Gaussian process regression in view of safe learning-based control.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies. This has enabled a plethora of successful implementations of Gaussian process-based model predictive control in a variety of applications over the last years. However, despite its evident practical effectiveness, there are still many open questions when attempting to analyze the associated optimal control problem theoretically and to exploit the full potential of Gaussian process regression in view of safe learning-based control.
11.
Zhang, Shuhao; Swevers, Jan
Robustified Time-optimal Point-to-point Motion Planning and Control under Uncertainty Working paper
2025.
@workingpaper{zhang2025robustified,
title = {Robustified Time-optimal Point-to-point Motion Planning and Control under Uncertainty},
author = {Shuhao Zhang and Jan Swevers },
doi = {https://doi.org/10.48550/arXiv.2501.14526},
year = {2025},
date = {2025-01-24},
abstract = {This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time grid, is seamlessly stitched with stage 2, which features a variable time grid. Stage 1 optimizes not only the nominal trajectory, but also feedback gains and corresponding state covariances, which robustify constraints in both stages. The outcome is a minimized uncertainty in stage 1 and a minimized total motion time for stage 2, both contributing to the time optimality and safety of the total motion. A timely replanning strategy is employed to handle changes in constraints and maintain feasibility, while a tailored iterative algorithm is proposed for efficient, real-time OCP execution.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time grid, is seamlessly stitched with stage 2, which features a variable time grid. Stage 1 optimizes not only the nominal trajectory, but also feedback gains and corresponding state covariances, which robustify constraints in both stages. The outcome is a minimized uncertainty in stage 1 and a minimized total motion time for stage 2, both contributing to the time optimality and safety of the total motion. A timely replanning strategy is employed to handle changes in constraints and maintain feasibility, while a tailored iterative algorithm is proposed for efficient, real-time OCP execution.
12.
Abbasi-Esfeden, Ramin; Nurkanovic, Armin; Diehl, Moritz; Patrinos, Panagiotis; Swevers, Jan
2025.
@workingpaper{abbasiesfeden2025efficientmixedintegerformulationiterative,
title = {An Efficient Mixed-Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints},
author = {Ramin Abbasi-Esfeden and Armin Nurkanovic and Moritz Diehl and Panagiotis Patrinos and Jan Swevers},
url = {https://arxiv.org/abs/2501.05158},
year = {2025},
date = {2025-01-09},
abstract = {This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a Sequence Optimization (SO) and a Switching Time Optimization (STO) -- the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for large numbers of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems and results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a Sequence Optimization (SO) and a Switching Time Optimization (STO) -- the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for large numbers of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems and results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.
13.
Kessler, Nicolas; Fagiano, Lorenzo
On gain scheduling trajectory stabilization for nonlinear systems: theoretical insights and experimental results Journal Article
In: International Journal of Robust and Nonlinear Control, 2025.
@article{kessler2024gain,
title = {On gain scheduling trajectory stabilization for nonlinear systems: theoretical insights and experimental results},
author = {Nicolas Kessler and Lorenzo Fagiano },
url = {https://onlinelibrary.wiley.com/doi/full/10.1002/rnc.7784},
doi = {https://doi.org/10.1002/rnc.7784},
year = {2025},
date = {2025-01-07},
journal = {International Journal of Robust and Nonlinear Control},
abstract = {Steering a nonlinear system from an initial state to a desired one is a common task in control. While a nominal trajectory can be obtained rather systematically using a model, for example via numerical optimization, heuristics, or reinforcement learning, the design of a computationally fast and reliable feedback control law that guarantees rev{bounded deviations around} the found trajectory can be much more involved.
An approach that does not require high online computational power and is well-accepted in industry is gain-scheduling.
The results presented here pertain to the rev{boundedness} guarantees and rev{the set of safe initial conditions} of gain scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions rev{for the existence of a robust polyquadratic Lyapunov function} to attempt the derivation of the desired gain-scheduled controller, via the solution of Linear Matrix Inequalities (LMIs). A result to estimate an ellipsoidal rev{set of safe initial conditions} is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can be used also to check/assess the rev{boundedness} properties obtained with an existing gain-scheduled law.
The approach is demonstrated experimentally on a small quadcopter, as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Steering a nonlinear system from an initial state to a desired one is a common task in control. While a nominal trajectory can be obtained rather systematically using a model, for example via numerical optimization, heuristics, or reinforcement learning, the design of a computationally fast and reliable feedback control law that guarantees rev{bounded deviations around} the found trajectory can be much more involved.
An approach that does not require high online computational power and is well-accepted in industry is gain-scheduling.
The results presented here pertain to the rev{boundedness} guarantees and rev{the set of safe initial conditions} of gain scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions rev{for the existence of a robust polyquadratic Lyapunov function} to attempt the derivation of the desired gain-scheduled controller, via the solution of Linear Matrix Inequalities (LMIs). A result to estimate an ellipsoidal rev{set of safe initial conditions} is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can be used also to check/assess the rev{boundedness} properties obtained with an existing gain-scheduled law.
The approach is demonstrated experimentally on a small quadcopter, as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.
An approach that does not require high online computational power and is well-accepted in industry is gain-scheduling.
The results presented here pertain to the rev{boundedness} guarantees and rev{the set of safe initial conditions} of gain scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions rev{for the existence of a robust polyquadratic Lyapunov function} to attempt the derivation of the desired gain-scheduled controller, via the solution of Linear Matrix Inequalities (LMIs). A result to estimate an ellipsoidal rev{set of safe initial conditions} is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can be used also to check/assess the rev{boundedness} properties obtained with an existing gain-scheduled law.
The approach is demonstrated experimentally on a small quadcopter, as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.
14.
Abbasi-Esfeden, Ramin; Plate, Christoph; Sager, Sebastian; Swevers, Jan
Dynamic Programming for Mixed Integer Optimal Control Problems with Dwell Time Constraints Working paper
2024.
@workingpaper{AbbasiEsfeden2024,
title = {Dynamic Programming for Mixed Integer Optimal Control Problems with Dwell Time Constraints},
author = {Ramin Abbasi-Esfeden and Christoph Plate and Sebastian Sager and Jan Swevers},
url = {http://dx.doi.org/10.2139/ssrn.5043263},
doi = {10.2139/ssrn.5043263},
year = {2024},
date = {2024-12-17},
journal = {Elsevier BV},
abstract = {This paper introduces Dynamic Programming (DP) as a method for solving the Combinatorial Integral Approximation (CIA) problem within the CIA decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs). Additionally, we incorporate general dwell time constraints into the DP framework. The proposed method is tested on three MIOCPs with a minimum dwell time constraint, and its performance is compared to the usage of the state-of-the-art general purpose solver GuRoBi (MILP) and to the tailored branch-and-bound (BnB) solver from the pycombina package. The results show that DP is more computationally efficient, and its flexible cost-to-go function formulation makes it suitable for handling cases where simple approximations of the relaxed solution are insufficient.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper introduces Dynamic Programming (DP) as a method for solving the Combinatorial Integral Approximation (CIA) problem within the CIA decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs). Additionally, we incorporate general dwell time constraints into the DP framework. The proposed method is tested on three MIOCPs with a minimum dwell time constraint, and its performance is compared to the usage of the state-of-the-art general purpose solver GuRoBi (MILP) and to the tailored branch-and-bound (BnB) solver from the pycombina package. The results show that DP is more computationally efficient, and its flexible cost-to-go function formulation makes it suitable for handling cases where simple approximations of the relaxed solution are insufficient.
15.
Prajapat, Manish; Lahr, Amon; Köhler, Johannes; Krause, Andreas; Zeilinger, Melanie N.
Towards Safe and Tractable Gaussian Process-Based MPC: Efficient Sampling within a Sequential Quadratic Programming Framework Proceedings Article
In: 2024 IEEE 63rd Conference on Decision and Control CDC, pp. 7458-7465, IEEE, Milan, Italy, 2024, ISBN: 9798350316339.
@inproceedings{prajapat_towards_2024,
title = {Towards Safe and Tractable Gaussian Process-Based MPC: Efficient Sampling within a Sequential Quadratic Programming Framework},
author = {Manish Prajapat and Amon Lahr and Johannes Köhler and Andreas Krause and Melanie N. Zeilinger},
doi = {10.1109/CDC56724.2024.10886350},
isbn = {9798350316339},
year = {2024},
date = {2024-12-16},
urldate = {2024-09-13},
booktitle = {2024 IEEE 63rd Conference on Decision and Control CDC},
pages = {7458-7465},
publisher = {IEEE},
address = {Milan, Italy},
abstract = {Learning uncertain dynamics models using Gaussian process (GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller’s safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GPMPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as realtime feasible computation times, using two numerical examples.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Learning uncertain dynamics models using Gaussian process (GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller’s safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GPMPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as realtime feasible computation times, using two numerical examples.
16.
Lahr, Amon; Näf, Joshua; Wabersich, Kim P.; Frey, Jonathan; Siehl, Pascal; Carron, Andrea; Diehl, Moritz; Zeilinger, Melanie N.
L4acados: Learning-based Models for Acados, Applied to Gaussian Process-Based Predictive Control Working paper
2024.
@workingpaper{lahr_l4acados_2024,
title = {L4acados: Learning-based Models for Acados, Applied to Gaussian Process-Based Predictive Control},
author = {Amon Lahr and Joshua Näf and Kim P. Wabersich and Jonathan Frey and Pascal Siehl and Andrea Carron and Moritz Diehl and Melanie N. Zeilinger},
doi = {10.48550/arXiv.2411.19258},
year = {2024},
date = {2024-11-28},
urldate = {2024-11-28},
abstract = {Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based residual models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based residual models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.
17.
Dong, Shiying; Ghezzi, Andrea; Harzer, Jakob; Frey, Jonathan; Gao, Bingzhao; Chen, Hong; Diehl, Moritz
Real-Time NMPC With Convex--Concave Constraints and Application to Eco-Driving Journal Article
In: IEEE Transactions on Control Systems Technology, 2024.
@article{dong2024real,
title = {Real-Time NMPC With Convex--Concave Constraints and Application to Eco-Driving},
author = {Shiying Dong and Andrea Ghezzi and Jakob Harzer and Jonathan Frey and Bingzhao Gao and Hong Chen and Moritz Diehl},
doi = {10.1109/TCST.2024.3494993},
year = {2024},
date = {2024-11-15},
journal = {IEEE Transactions on Control Systems Technology},
abstract = {In this brief, we propose a novel real-time numerical algorithm for solving nonlinear model predictive control (NMPC) with convex–concave constraints, which arise in various practical applications. Instead of requiring full convergence for each problem at every sampling time, the proposed algorithm, called real-time iteration sequential convex programming (RTI-SCP), solves only one convex subproblem but iterates as the problem evolves. Compared with previous methods, the RTI-SCP adopts a more refined approach by linearizing only the concave components of the constraints. It retains and efficiently utilizes all the underlying convex structures, thereby transforming subproblems into structured forms that can be solved using the existing tools. In addition, to the best of our knowledge, the widely investigated eco-driving control strategy for autonomous vehicles is now formulated for the first time into a convex–concave programming problem with strong theoretical properties. Eventually, the experimental results demonstrate that the proposed strategy can improve computational efficiency and overall control performance, and it is suitable for real-time implementation.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this brief, we propose a novel real-time numerical algorithm for solving nonlinear model predictive control (NMPC) with convex–concave constraints, which arise in various practical applications. Instead of requiring full convergence for each problem at every sampling time, the proposed algorithm, called real-time iteration sequential convex programming (RTI-SCP), solves only one convex subproblem but iterates as the problem evolves. Compared with previous methods, the RTI-SCP adopts a more refined approach by linearizing only the concave components of the constraints. It retains and efficiently utilizes all the underlying convex structures, thereby transforming subproblems into structured forms that can be solved using the existing tools. In addition, to the best of our knowledge, the widely investigated eco-driving control strategy for autonomous vehicles is now formulated for the first time into a convex–concave programming problem with strong theoretical properties. Eventually, the experimental results demonstrate that the proposed strategy can improve computational efficiency and overall control performance, and it is suitable for real-time implementation.
18.
Wang, Renzi; Acerbo, Flavia Sofia; Son, Tong Duy; Patrinos, Panagiotis
Imitation Learning from Observations: An Autoregressive Mixture of Experts Approach Working paper
2024.
@workingpaper{wang2024imitation,
title = {Imitation Learning from Observations: An Autoregressive Mixture of Experts Approach},
author = {Renzi Wang and Flavia Sofia Acerbo and Tong Duy Son and Panagiotis Patrinos},
url = {https://doi.org/10.48550/arXiv.2411.08232
},
year = {2024},
date = {2024-11-12},
abstract = {This paper presents a novel approach to imitation learning from observations, where an autoregressive mixture of experts model is deployed to fit the underlying policy. The parameters of the model are learned via a two-stage framework. By leveraging the existing dynamics knowledge, the first stage of the framework estimates the control input sequences and hence reduces the problem complexity. At the second stage, the policy is learned by solving a regularized maximum-likelihood estimation problem using the estimated control input sequences. We further extend the learning procedure by incorporating a Lyapunov stability constraint to ensure asymptotic stability of the identified model, for accurate multi-step predictions. The effectiveness of the proposed framework is validated using two autonomous driving datasets collected from human demonstrations, demonstrating its practical applicability in modelling complex nonlinear dynamics.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
This paper presents a novel approach to imitation learning from observations, where an autoregressive mixture of experts model is deployed to fit the underlying policy. The parameters of the model are learned via a two-stage framework. By leveraging the existing dynamics knowledge, the first stage of the framework estimates the control input sequences and hence reduces the problem complexity. At the second stage, the policy is learned by solving a regularized maximum-likelihood estimation problem using the estimated control input sequences. We further extend the learning procedure by incorporating a Lyapunov stability constraint to ensure asymptotic stability of the identified model, for accurate multi-step predictions. The effectiveness of the proposed framework is validated using two autonomous driving datasets collected from human demonstrations, demonstrating its practical applicability in modelling complex nonlinear dynamics.
19.
Zhang, Yuan; Hoffman, Jasper; Boedecker, Joschka
UDUC: An Uncertainty-driven Approach for Learning-based Robust Control Proceedings Article
In: ECAI 2024 - 27th European Conference on Artificial Intelligence - Including 13th Conference on Prestigious Applications of Intelligent Systems (PAIS 2024), pp. 4402-4409, IOS Press, Santiago de Compostela, Spain, 2024.
@inproceedings{zhang2024uduc,
title = {UDUC: An Uncertainty-driven Approach for Learning-based Robust Control},
author = {Yuan Zhang and Jasper Hoffman and Joschka Boedecker},
url = {https://arxiv.org/abs/2405.02598},
doi = {10.3233/FAIA241018},
year = {2024},
date = {2024-10-24},
urldate = {2024-10-24},
booktitle = {ECAI 2024 - 27th European Conference on Artificial Intelligence - Including 13th Conference on Prestigious Applications of Intelligent Systems (PAIS 2024)},
volume = {392},
pages = {4402-4409},
publisher = {IOS Press},
address = {Santiago de Compostela, Spain},
series = {Frontiers in Artificial Intelligence and Applications},
abstract = {Learning-based techniques have become popular in both model predictive control (MPC) and reinforcement learning (RL). Probabilistic ensemble (PE) models offer a promising approach for modelling system dynamics, showcasing the ability to capture uncertainty and scalability in high-dimensional control scenarios. However, PE models are susceptible to mode collapse, resulting in non-robust control when faced with environments slightly different from the training set. In this paper, we introduce the uncertainty-driven robust control (UDUC) loss as an alternative objective for training PE models, drawing inspiration from contrastive learning. We analyze the robustness of the UDUC loss through the lens of robust optimization and evaluate its performance on the challenging real-world reinforcement learning (RWRL) benchmark, which involves significant environmental mismatches between the training and testing environments.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Learning-based techniques have become popular in both model predictive control (MPC) and reinforcement learning (RL). Probabilistic ensemble (PE) models offer a promising approach for modelling system dynamics, showcasing the ability to capture uncertainty and scalability in high-dimensional control scenarios. However, PE models are susceptible to mode collapse, resulting in non-robust control when faced with environments slightly different from the training set. In this paper, we introduce the uncertainty-driven robust control (UDUC) loss as an alternative objective for training PE models, drawing inspiration from contrastive learning. We analyze the robustness of the UDUC loss through the lens of robust optimization and evaluate its performance on the challenging real-world reinforcement learning (RWRL) benchmark, which involves significant environmental mismatches between the training and testing environments.
20.
Acerbo, Flavia Sofia; Swevers, Jan; Tuytelaars, Tinne; Son, Tong Duy
Driving from Vision through Differentiable Optimal Control Proceedings Article
In: 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2153-0866, IEEE, Abu Dhabi, United Arab Emirates, 2024, ISBN: 979-8-3503-7770-5.
@inproceedings{acerbo24drividoc,
title = {Driving from Vision through Differentiable Optimal Control},
author = {Flavia Sofia Acerbo and Jan Swevers and Tinne Tuytelaars and Tong Duy Son},
url = {https://doi.org/10.48550/arXiv.2403.15102
},
doi = {10.1109/IROS58592.2024.10802306},
isbn = {979-8-3503-7770-5},
year = {2024},
date = {2024-10-01},
booktitle = {2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
pages = {2153-0866},
publisher = {IEEE},
address = {Abu Dhabi, United Arab Emirates},
abstract = {This paper proposes DriViDOC: a framework for Driving from Vision through Differentiable Optimal Control, and its application to learn autonomous driving controllers from human demonstrations. DriViDOC combines the automatic inference of relevant features from camera frames with the properties of nonlinear model predictive control (NMPC), such as constraint satisfaction. Our approach leverages the differentiability of parametric NMPC, allowing for end-to-end learning of the driving model from images to control. The model is trained on an offline dataset comprising various human demonstrations collected on a motion-base driving simulator. During online testing, the model demonstrates successful imitation of different driving styles, and the interpreted NMPC parameters provide insights into the achievement of specific driving behaviors. Our experimental results show that DriViDOC outperforms other methods involving NMPC and neural networks, exhibiting an average improvement of 20% in imitation scores.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
This paper proposes DriViDOC: a framework for Driving from Vision through Differentiable Optimal Control, and its application to learn autonomous driving controllers from human demonstrations. DriViDOC combines the automatic inference of relevant features from camera frames with the properties of nonlinear model predictive control (NMPC), such as constraint satisfaction. Our approach leverages the differentiability of parametric NMPC, allowing for end-to-end learning of the driving model from images to control. The model is trained on an offline dataset comprising various human demonstrations collected on a motion-base driving simulator. During online testing, the model demonstrates successful imitation of different driving styles, and the interpreted NMPC parameters provide insights into the achievement of specific driving behaviors. Our experimental results show that DriViDOC outperforms other methods involving NMPC and neural networks, exhibiting an average improvement of 20% in imitation scores.