Publications
41.
Løwenstein, Kristoffer Fink; Bernardini, Daniele; Patrinos, Panagiotis
QPALM-OCP: A Newton-type Proximal Augmented Lagrangian tailored for Quadratic Programs arising in Model Predictive Control Journal Article
In: IEEE Control Systems Letters, 2024, ISSN: 2475-1456, (Submitted to the 63rd IEEE Conference on Decision and Control 2024 (CDC)).
@article{Lowenstein2024QPALMOCP,
title = {QPALM-OCP: A Newton-type Proximal Augmented Lagrangian tailored for Quadratic Programs arising in Model Predictive Control},
author = {Kristoffer Fink Løwenstein and Daniele Bernardini and Panagiotis Patrinos},
doi = {10.1109/LCSYS.2024.3410638},
issn = {2475-1456},
year = {2024},
date = {2024-06-06},
urldate = {2024-04-02},
journal = {IEEE Control Systems Letters},
abstract = {In Model Predictive Control (MPC) fast and reliable Quadratic Programming (QP) solvers are of fundamental importance. The inherent structure of the subsequent Optimal Control Problems (OCPs) can lead to substantial performance improvements if exploited. Therefore, we present a structure-exploiting proximal augmented Lagrangian based solver extending the general-purpose QP-solver QPALM. Our solver relies on semismooth Newton iterates to solve the inner sub-problem while directly accounting for the OCP structure via efficient and sparse matrix factorizations. The matrices to be factorized depends on the active set and therefore low-rank factorization updates can be employed like in active-set methods resulting in cheap iterates. We benchmark our solver against other state-of-the-art QP-solvers and our algorithm compare favorably against these solvers},
note = {Submitted to the 63rd IEEE Conference on Decision and Control 2024 (CDC)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In Model Predictive Control (MPC) fast and reliable Quadratic Programming (QP) solvers are of fundamental importance. The inherent structure of the subsequent Optimal Control Problems (OCPs) can lead to substantial performance improvements if exploited. Therefore, we present a structure-exploiting proximal augmented Lagrangian based solver extending the general-purpose QP-solver QPALM. Our solver relies on semismooth Newton iterates to solve the inner sub-problem while directly accounting for the OCP structure via efficient and sparse matrix factorizations. The matrices to be factorized depends on the active set and therefore low-rank factorization updates can be employed like in active-set methods resulting in cheap iterates. We benchmark our solver against other state-of-the-art QP-solvers and our algorithm compare favorably against these solvers
42.
Reiter, Rudolf; Ghezzi, Andrea; Baumgärtner, Katrin; Hoffman, Jasper; McAllister, Robert D; Diehl, Moritz
AC4MPC: Actor-Critic Reinforcement Learning for Nonlinear Model Predictive Control Working paper
2024.
@workingpaper{reiter2024ac4mpc,
title = {AC4MPC: Actor-Critic Reinforcement Learning for Nonlinear Model Predictive Control},
author = {Rudolf Reiter and Andrea Ghezzi and Katrin Baumgärtner and Jasper Hoffman and Robert D McAllister and Moritz Diehl },
url = {https://doi.org/10.48550/arXiv.2406.03995},
year = {2024},
date = {2024-06-06},
abstract = {Ac{MPC} and ac{RL} are two powerful control strategies with, arguably, complementary advantages. In this work, we show how actor-critic ac{RL} techniques can be leveraged to improve the performance of ac{MPC}. The ac{RL} critic is used as an approximation of the optimal value function, and an actor roll-out provides an initial guess for primal variables of the ac{MPC}. A parallel control architecture is proposed where each ac{MPC} instance is solved twice for different initial guesses. Besides the actor roll-out initialization, a shifted initialization from the previous solution is used. Thereafter, the actor and the critic are again used to approximately evaluate the infinite horizon cost of these trajectories. The control actions from the lowest-cost trajectory are applied to the system at each time step. We establish that the proposed algorithm is guaranteed to outperform the original ac{RL} policy plus an error term that depends on the accuracy of the critic and decays with the horizon length of the ac{MPC} formulation. Moreover, we do not require globally optimal solutions for these guarantees to hold. The approach is demonstrated on an illustrative toy example and an ac{AD} overtaking scenario.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Ac{MPC} and ac{RL} are two powerful control strategies with, arguably, complementary advantages. In this work, we show how actor-critic ac{RL} techniques can be leveraged to improve the performance of ac{MPC}. The ac{RL} critic is used as an approximation of the optimal value function, and an actor roll-out provides an initial guess for primal variables of the ac{MPC}. A parallel control architecture is proposed where each ac{MPC} instance is solved twice for different initial guesses. Besides the actor roll-out initialization, a shifted initialization from the previous solution is used. Thereafter, the actor and the critic are again used to approximately evaluate the infinite horizon cost of these trajectories. The control actions from the lowest-cost trajectory are applied to the system at each time step. We establish that the proposed algorithm is guaranteed to outperform the original ac{RL} policy plus an error term that depends on the accuracy of the critic and decays with the horizon length of the ac{MPC} formulation. Moreover, we do not require globally optimal solutions for these guarantees to hold. The approach is demonstrated on an illustrative toy example and an ac{AD} overtaking scenario.
43.
Frey, Jonathan; Gao, Yunfan; Messerer, Florian; Lahr, Amon; Zeilinger, Melanie N.; Diehl, Moritz
Efficient Zero-Order Robust Optimization for Real-Time Model Predictive Control with Acados Proceedings Article
In: 2024 European Control Conference (ECC), IEEE, Stockholm, Sweden, 2024, ISBN: 978-3-9071-4410-7.
@inproceedings{frey_efficient_2023,
title = {Efficient Zero-Order Robust Optimization for Real-Time Model Predictive Control with Acados},
author = {Jonathan Frey and Yunfan Gao and Florian Messerer and Amon Lahr and Melanie N. Zeilinger and Moritz Diehl},
doi = {10.23919/ECC64448.2024.10591148},
isbn = {978-3-9071-4410-7},
year = {2024},
date = {2024-06-03},
urldate = {2023-12-18},
booktitle = {2024 European Control Conference (ECC)},
publisher = {IEEE},
address = {Stockholm, Sweden},
abstract = {Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm mitigates the computational cost of uncertainty-aware MPC by propagating the uncertainties separately from the nominal dynamics. This paper details the combination of zoRO with the real-time iteration (RTI) scheme and presents an efficient open-source implementation in acados, utilizing BLASFEO for the linear algebra operations. In addition to the scaling advantages posed by the zoRO algorithm, the efficient implementation drastically reduces the computational overhead, and, combined with an RTI scheme, enables the use of tube-based MPC for a wider range of applications. The flexibility, usability and effectiveness of the proposed implementation is demonstrated on two examples. On the practical example of a differential drive robot, the proposed implementation results in a tenfold reduction of computation time with respect to the previously available zoRO implementation.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm mitigates the computational cost of uncertainty-aware MPC by propagating the uncertainties separately from the nominal dynamics. This paper details the combination of zoRO with the real-time iteration (RTI) scheme and presents an efficient open-source implementation in acados, utilizing BLASFEO for the linear algebra operations. In addition to the scaling advantages posed by the zoRO algorithm, the efficient implementation drastically reduces the computational overhead, and, combined with an RTI scheme, enables the use of tube-based MPC for a wider range of applications. The flexibility, usability and effectiveness of the proposed implementation is demonstrated on two examples. On the practical example of a differential drive robot, the proposed implementation results in a tenfold reduction of computation time with respect to the previously available zoRO implementation.
44.
Simpson, Léo; Asprion, Jonas; Muntwiler, Simon; Köhler, Johannes; Diehl, Moritz
Parallelizable Parametric Nonlinear System Identification via tuning of a Moving Horizon State Estimator Proceedings Article Forthcoming
In: Forthcoming, (Accepted to the 63rd IEEE Conference on Decision and Control 2024 (CDC)).
@inproceedings{Simpson2024Parallelizable,
title = {Parallelizable Parametric Nonlinear System Identification via tuning of a Moving Horizon State Estimator},
author = {Léo Simpson and Jonas Asprion and Simon Muntwiler and Johannes Köhler and Moritz Diehl},
doi = {https://doi.org/10.48550/arXiv.2403.17858},
year = {2024},
date = {2024-05-29},
urldate = {2024-05-29},
abstract = {This paper introduces a novel optimization-based approach for parametric nonlinear system identification. Building upon the prediction error method framework, traditionally used for linear system identification, we extend its capabilities to nonlinear systems. The predictions are computed using a moving horizon state estimator with a constant arrival cost. Eventually, both the system parameters and the arrival cost are estimated by minimizing the sum of the squared prediction errors. Since the predictions are induced by the state estimator, the method can be viewed as the tuning of a state estimator, based on its predictive capacities. The present extension of the prediction error method not only enhances performance for nonlinear systems but also enables learning from multiple trajectories with unknown initial states, broadening its applicability in practical scenarios. Additionally, the novel formulation leaves room for the design of efficient and parallelizable optimization algorithms, since each output prediction only depends on a fixed window of past actions and measurements. In the special case of linear time-invariant systems, we show an important property of the proposed method which suggests asymptotic consistency under reasonable assumptions. Numerical examples illustrate the effectiveness and practicality of the approach, and one of the examples also highlights the necessity for the arrival cost.},
note = {Accepted to the 63rd IEEE Conference on Decision and Control 2024 (CDC)},
keywords = {},
pubstate = {forthcoming},
tppubtype = {inproceedings}
}
This paper introduces a novel optimization-based approach for parametric nonlinear system identification. Building upon the prediction error method framework, traditionally used for linear system identification, we extend its capabilities to nonlinear systems. The predictions are computed using a moving horizon state estimator with a constant arrival cost. Eventually, both the system parameters and the arrival cost are estimated by minimizing the sum of the squared prediction errors. Since the predictions are induced by the state estimator, the method can be viewed as the tuning of a state estimator, based on its predictive capacities. The present extension of the prediction error method not only enhances performance for nonlinear systems but also enables learning from multiple trajectories with unknown initial states, broadening its applicability in practical scenarios. Additionally, the novel formulation leaves room for the design of efficient and parallelizable optimization algorithms, since each output prediction only depends on a fixed window of past actions and measurements. In the special case of linear time-invariant systems, we show an important property of the proposed method which suggests asymptotic consistency under reasonable assumptions. Numerical examples illustrate the effectiveness and practicality of the approach, and one of the examples also highlights the necessity for the arrival cost.
45.
Bourkhissi, Lahcen El; Necoara, Ion
Convergence rates for an inexact linearized ADMM for nonsmooth optimization with nonlinear equality constraints Working paper
2024, (Under review).
@workingpaper{bourkhissi2024convergence,
title = {Convergence rates for an inexact linearized ADMM for nonsmooth optimization with nonlinear equality constraints},
author = {Lahcen El Bourkhissi and Ion Necoara},
year = {2024},
date = {2024-05-29},
urldate = {2024-05-29},
note = {Under review},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
46.
Wang, Jianhong; Li, Yang; Zhang, Yuan; Pan, Wei; Kaski, Samuel
Open Ad Hoc Teamwork with Cooperative Game Theory Proceedings Article
In: Forty-first International Conference on Machine Learning, 2024.
@inproceedings{wang2024open,
title = {Open Ad Hoc Teamwork with Cooperative Game Theory},
author = {Jianhong Wang and Yang Li and Yuan Zhang and Wei Pan and Samuel Kaski},
url = {https://openreview.net/forum?id=RlibRvH4B4},
year = {2024},
date = {2024-05-09},
urldate = {2024-05-09},
booktitle = {Forty-first International Conference on Machine Learning},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
47.
Zhang, Yuan; Deekshith, Umashankar; Wang, Jianhong; Boedecker, Joschka
LCPPO: An Efficient Multi-agent Reinforcement Learning Algorithm on Complex Railway Network Proceedings Article
In: 34th International Conference on Automated Planning and Scheduling, 2024.
@inproceedings{zhanglcppo,
title = {LCPPO: An Efficient Multi-agent Reinforcement Learning Algorithm on Complex Railway Network},
author = {Yuan Zhang and Umashankar Deekshith and Jianhong Wang and Joschka Boedecker},
url = {https://openreview.net/forum?id=gylH3hNASm},
year = {2024},
date = {2024-05-09},
urldate = {2024-05-09},
booktitle = {34th International Conference on Automated Planning and Scheduling},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
48.
Shengchao, Yan; Zhang, Yuan; Zhang, Bohe; Boedecker, Joschka; Burgard, Wolfram
Learning Continuous Control with Geometric Regularity from Robot Intrinsic Symmetry Proceedings Article
In: 2024 IEEE International Conference on Robotics and Automation ICRA, 2024.
@inproceedings{yan2023geometricb,
title = {Learning Continuous Control with Geometric Regularity from Robot Intrinsic Symmetry},
author = {Yan Shengchao and Yuan Zhang and Bohe Zhang and Joschka Boedecker and Wolfram Burgard},
url = {https://arxiv.org/abs/2306.16316},
year = {2024},
date = {2024-05-09},
urldate = {2024-05-09},
booktitle = {2024 IEEE International Conference on Robotics and Automation ICRA},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
49.
Ghezzi, Andrea; Roy, Wim Van; Sager, Sebastian; Diehl, Moritz
A Sequential Benders-based Mixed-Integer Quadratic Programming Algorithm Working paper
2024.
@workingpaper{ghezzi2024sequential,
title = {A Sequential Benders-based Mixed-Integer Quadratic Programming Algorithm},
author = {Andrea Ghezzi and Wim Van Roy and Sebastian Sager and Moritz Diehl},
url = {https://doi.org/10.48550/arXiv.2404.11786},
year = {2024},
date = {2024-04-17},
abstract = {For continuous decision spaces, nonlinear programs (NLPs) can be efficiently solved via sequential quadratic programming (SQP) and, more generally, sequential convex programming (SCP). These algorithms linearize only the nonlinear equality constraints and keep the outer convex structure of the problem intact. The aim of the presented sequential mixed-integer quadratic programming (MIQP) algorithm for mixed-integer nonlinear problems (MINLPs) is to extend the SQP/SCP methodology to MINLPs and leverage the availability of efficient MIQP solvers. The algorithm employs a three-step method in each iterate: First, the MINLP is linearized at a given iterate. Second, an MIQP with its feasible set restricted to a specific region around the current linearization point is formulated and solved. Third, the integer variables obtained from the MIQP solution are fixed, and only an NLP in the continuous variables is solved. The outcome of the third step is compared to previous iterates, and the best iterate so far is used as a linearization point in the next iterate. Crucially, the objective values and derivatives from all previous iterates are used to formulate the polyhedral region in the second step. The linear inequalities that define the region build on concepts from generalized Benders' decomposition for MINLPs. Although the presented MINLP algorithm is a heuristic method without any global optimality guarantee, it converges to the exact integer solution when applied to convex MINLP with a linear outer structure. The conducted numerical experiments demonstrate that the proposed algorithm is competitive with other open-source solvers for MINLP. Finally, we solve two mixed-integer optimal control problems (MIOCPs) transcribed into MINLPs via direct methods, showing that the presented algorithm can effectively deal with nonlinear equality constraints, a major hurdle for generic MINLP solvers.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
For continuous decision spaces, nonlinear programs (NLPs) can be efficiently solved via sequential quadratic programming (SQP) and, more generally, sequential convex programming (SCP). These algorithms linearize only the nonlinear equality constraints and keep the outer convex structure of the problem intact. The aim of the presented sequential mixed-integer quadratic programming (MIQP) algorithm for mixed-integer nonlinear problems (MINLPs) is to extend the SQP/SCP methodology to MINLPs and leverage the availability of efficient MIQP solvers. The algorithm employs a three-step method in each iterate: First, the MINLP is linearized at a given iterate. Second, an MIQP with its feasible set restricted to a specific region around the current linearization point is formulated and solved. Third, the integer variables obtained from the MIQP solution are fixed, and only an NLP in the continuous variables is solved. The outcome of the third step is compared to previous iterates, and the best iterate so far is used as a linearization point in the next iterate. Crucially, the objective values and derivatives from all previous iterates are used to formulate the polyhedral region in the second step. The linear inequalities that define the region build on concepts from generalized Benders' decomposition for MINLPs. Although the presented MINLP algorithm is a heuristic method without any global optimality guarantee, it converges to the exact integer solution when applied to convex MINLP with a linear outer structure. The conducted numerical experiments demonstrate that the proposed algorithm is competitive with other open-source solvers for MINLP. Finally, we solve two mixed-integer optimal control problems (MIOCPs) transcribed into MINLPs via direct methods, showing that the presented algorithm can effectively deal with nonlinear equality constraints, a major hurdle for generic MINLP solvers.
50.
Løwenstein, Kristoffer Fink; Bernardini, Daniele; Bemporad, Alberto; Fagiano, Lorenzo
Physics-Informed Online Learning by Moving Horizon Estimation: Learning Recurrent Neural Networks in Gray-box Models Proceedings Article
In: 8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024, pp. 78-85, IFAC-PapersOnLine, 2024, ISSN: 2405-8963.
@inproceedings{Lowenstein2024PhysicsInformedRNN,
title = {Physics-Informed Online Learning by Moving Horizon Estimation: Learning Recurrent Neural Networks in Gray-box Models},
author = {Kristoffer Fink Løwenstein and Daniele Bernardini and Alberto Bemporad and Lorenzo Fagiano },
url = {https://www.sciencedirect.com/science/article/pii/S2405896324013922},
doi = {10.1016/j.ifacol.2024.09.013},
issn = {2405-8963},
year = {2024},
date = {2024-04-02},
urldate = {2024-04-02},
booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},
volume = {58},
number = {18},
pages = {78-85},
publisher = {IFAC-PapersOnLine},
abstract = {In Model Predictive Control (MPC) closed-loop performance heavily depends on the quality of the underlying prediction model, where such a model must be accurate and yet simple. A key feature in modern MPC applications is the potential for online model adaptation to cope with time-varying changes, part-to-part variations, and complex features of the system dynamics not caught by models derived from first principles. In this paper, we propose to use a physics-informed, or gray-box, model that extends the physics-based model with a data-driven component, namely a Recurrent Neural Network (RNN). Relying on physics-informed models allows for a rather limited size of the RNN, thereby enhancing online applicability compared to pure black-box models. This work presents a method based on Moving Horizon Estimation (MHE) for simultaneous state estimation and learning of the RNN sub-model, a potentially challenging issue due to limited information available in noisy input-output data and lack of knowledge of the internal state of the RNN. We provide a case study on a quadruple tank benchmark showing how the method can cope with part-to-part variations.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
In Model Predictive Control (MPC) closed-loop performance heavily depends on the quality of the underlying prediction model, where such a model must be accurate and yet simple. A key feature in modern MPC applications is the potential for online model adaptation to cope with time-varying changes, part-to-part variations, and complex features of the system dynamics not caught by models derived from first principles. In this paper, we propose to use a physics-informed, or gray-box, model that extends the physics-based model with a data-driven component, namely a Recurrent Neural Network (RNN). Relying on physics-informed models allows for a rather limited size of the RNN, thereby enhancing online applicability compared to pure black-box models. This work presents a method based on Moving Horizon Estimation (MHE) for simultaneous state estimation and learning of the RNN sub-model, a potentially challenging issue due to limited information available in noisy input-output data and lack of knowledge of the internal state of the RNN. We provide a case study on a quadruple tank benchmark showing how the method can cope with part-to-part variations.
51.
Meza, Gonzalo; Løwenstein, Kristoffer Fink; Fagiano, Lorenzo
Obstacle avoidance for a robotic manipulator with linear-quadratic Model Predictive Control Proceedings Article
In: 2024 IEEE 20th International Conference on Automation Science and Engineering (CASE 2024), pp. 3365-3370, 2024.
@inproceedings{Meza2024ObstacleMPC,
title = {Obstacle avoidance for a robotic manipulator with linear-quadratic Model Predictive Control},
author = {Gonzalo Meza and Kristoffer Fink Løwenstein and Lorenzo Fagiano },
doi = {10.1109/CASE59546.2024.10711546},
year = {2024},
date = {2024-04-02},
urldate = {2024-04-02},
booktitle = {2024 IEEE 20th International Conference on Automation Science and Engineering (CASE 2024)},
pages = {3365-3370},
abstract = {The problem of moving a six-degrees-of-freedom manipulator in an environment with unknown obstacles is considered. The manipulator is assumed to be equipped with an exteroceptive sensor that provides a partial sampling of the surroundings. A hierarchical control layout is proposed: in the outer layer, a path planner generates an obstacle free trajectory based on the available local information; in the inner layer, a Model-Predictive Controller formulated in the joint space tracks the trajectory while reactively avoiding unseen obstacles at a higher rate. By constructing a polytopic under-approximation of the free environment end employing a suitable estimate of the Jacobian matrix of the manipulator, the predictive controller features a convex quadratic cost and linear constraints, thus requiring the solution of a quadratic program at each time step. The proposed method is evaluated on the kinematic model of a MyCobot280 robotic arm, showing the potential for real-time feasibility.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
The problem of moving a six-degrees-of-freedom manipulator in an environment with unknown obstacles is considered. The manipulator is assumed to be equipped with an exteroceptive sensor that provides a partial sampling of the surroundings. A hierarchical control layout is proposed: in the outer layer, a path planner generates an obstacle free trajectory based on the available local information; in the inner layer, a Model-Predictive Controller formulated in the joint space tracks the trajectory while reactively avoiding unseen obstacles at a higher rate. By constructing a polytopic under-approximation of the free environment end employing a suitable estimate of the Jacobian matrix of the manipulator, the predictive controller features a convex quadratic cost and linear constraints, thus requiring the solution of a quadratic program at each time step. The proposed method is evaluated on the kinematic model of a MyCobot280 robotic arm, showing the potential for real-time feasibility.
52.
Messerer, Florian; Baumgärtner, Katrin; Lucia, Sergio; Diehl, Moritz
Fourth-order suboptimality of nominal model predictive control in the presence of uncertainty Journal Article
In: IEEE Control Systems Letters, vol. 8, pp. 508-513, 2024.
@article{messerer2024fourthorder,
title = {Fourth-order suboptimality of nominal model predictive control in the presence of uncertainty},
author = {Florian Messerer and Katrin Baumgärtner and Sergio Lucia and Moritz Diehl},
doi = {10.1109/LCSYS.2024.3396611},
year = {2024},
date = {2024-03-08},
urldate = {2024-03-08},
journal = {IEEE Control Systems Letters},
volume = {8},
pages = {508-513},
abstract = {We investigate the suboptimality resulting from the application of nominal model predictive control (MPC) to a nonlinear discrete time stochastic system. The suboptimality is defined with respect to the corresponding stochastic optimal control problem (OCP) that minimizes the expected cost of the closed loop system. In this context, nominal MPC corresponds to a form of certainty-equivalent control (CEC). We prove that, in a smooth and unconstrained setting, the suboptimality growth is of fourth order with respect to the level of uncertainty, a parameter which we can think of as a standard deviation. This implies that the suboptimality does not grow very quickly as the level of uncertainty is increased, providing further insight into the practical success of nominal MPC. Similarly, the difference between the optimal and suboptimal control inputs is of second order. We illustrate the result on a simple numerical example, which we also use to show how the proven relationship may cease to hold in the presence of state constraints.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate the suboptimality resulting from the application of nominal model predictive control (MPC) to a nonlinear discrete time stochastic system. The suboptimality is defined with respect to the corresponding stochastic optimal control problem (OCP) that minimizes the expected cost of the closed loop system. In this context, nominal MPC corresponds to a form of certainty-equivalent control (CEC). We prove that, in a smooth and unconstrained setting, the suboptimality growth is of fourth order with respect to the level of uncertainty, a parameter which we can think of as a standard deviation. This implies that the suboptimality does not grow very quickly as the level of uncertainty is increased, providing further insight into the practical success of nominal MPC. Similarly, the difference between the optimal and suboptimal control inputs is of second order. We illustrate the result on a simple numerical example, which we also use to show how the proven relationship may cease to hold in the presence of state constraints.
53.
Xie, Jing; Bonassi, Fabio; Scattolini, Riccardo
Internal Model Control design for systems learned by Control Affine Neural Nonlinear Autoregressive Exogenous Models Working paper Forthcoming
Forthcoming, (Accepted by IEEE Transactions on Automation Science and Engineering).
@workingpaper{xie2024internal,
title = {Internal Model Control design for systems learned by Control Affine Neural Nonlinear Autoregressive Exogenous Models},
author = {Jing Xie and Fabio Bonassi and Riccardo Scattolini},
url = {https://arxiv.org/abs/2402.05607},
year = {2024},
date = {2024-02-13},
urldate = {2024-02-13},
abstract = {This paper explores the use of Control Affine Neural Nonlinear AutoRegressive eXogenous (CA-NNARX) models for nonlinear system identification and model-based control design. The idea behind this architecture is to match the known control-affine structure of the system to achieve improved performance. Coherently with recent literature of neural networks for data-driven control, we first analyze the stability properties of CA-NNARX models, devising sufficient conditions for their incremental Input-to-State Stability (𝛿ISS) that can be enforced at the model training stage. The model's stability property is then leveraged to design a stable Internal Model Control (IMC) architecture. The proposed control scheme is tested on a real Quadruple Tank benchmark system to address the output reference tracking problem. The results achieved show that (i) the modeling accuracy of CA-NNARX is superior to the one of a standard NNARX model for given weight size and training epochs, (ii) the proposed IMC law provides performance comparable to the ones of a standard Model Predictive Controller (MPC) at a significantly lower computational burden, and (iii) the 𝛿ISS of the model is beneficial to the closed-loop performance.}},
note = {Accepted by IEEE Transactions on Automation Science and Engineering},
keywords = {},
pubstate = {forthcoming},
tppubtype = {workingpaper}
}
This paper explores the use of Control Affine Neural Nonlinear AutoRegressive eXogenous (CA-NNARX) models for nonlinear system identification and model-based control design. The idea behind this architecture is to match the known control-affine structure of the system to achieve improved performance. Coherently with recent literature of neural networks for data-driven control, we first analyze the stability properties of CA-NNARX models, devising sufficient conditions for their incremental Input-to-State Stability (𝛿ISS) that can be enforced at the model training stage. The model's stability property is then leveraged to design a stable Internal Model Control (IMC) architecture. The proposed control scheme is tested on a real Quadruple Tank benchmark system to address the output reference tracking problem. The results achieved show that (i) the modeling accuracy of CA-NNARX is superior to the one of a standard NNARX model for given weight size and training epochs, (ii) the proposed IMC law provides performance comparable to the ones of a standard Model Predictive Controller (MPC) at a significantly lower computational burden, and (iii) the 𝛿ISS of the model is beneficial to the closed-loop performance.}
54.
Zhang, Shuhao; Swevers, Jan
Two-stage Time-optimal Motion Planning Presentation
07.02.2024, (Abstract at the 2024 Benelux Meeting ).
@misc{lirias4141067,
title = {Two-stage Time-optimal Motion Planning},
author = {Shuhao Zhang and Jan Swevers},
year = {2024},
date = {2024-02-07},
urldate = {2024-02-07},
note = {Abstract at the 2024 Benelux Meeting },
keywords = {},
pubstate = {published},
tppubtype = {presentation}
}
55.
Simpson, Léo; Ghezzi, Andrea; Asprion, Jonas; Diehl, Moritz
An Efficient Method for the Joint Estimation of System Parameters and Noise Covariances for Linear Time-Variant Systems Proceedings Article
In: 2023 Conference of Decision and Control (CDC) , pp. 4524-4529, IEEE, Singapore, Singapore, 2024, ISSN: 2576-2370.
@inproceedings{Simpson2023EMJE,
title = {An Efficient Method for the Joint Estimation of System Parameters and Noise Covariances for Linear Time-Variant Systems },
author = {Léo Simpson and Andrea Ghezzi and Jonas Asprion and Moritz Diehl},
url = {https://arxiv.org/abs/2211.12302},
doi = {10.1109/CDC49753.2023.10383686},
issn = {2576-2370},
year = {2024},
date = {2024-01-19},
urldate = {2024-01-19},
booktitle = {2023 Conference of Decision and Control (CDC) },
pages = {4524-4529},
publisher = {IEEE},
address = {Singapore, Singapore},
abstract = {We present an optimization-based method for the joint estimation of system parameters and noise covariances of linear time-variant systems. Given measured data, this method maximizes the likelihood of the parameters. We solve the optimization problem of interest via a novel structure-exploiting solver. We present the advantages of the proposed approach over commonly used methods in the framework of Moving Horizon Estimation. Finally, we show the performance of the method through numerical simulations on a realistic example of a thermal system. In this example, the method can successfully estimate the model parameters in a short computational time.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
We present an optimization-based method for the joint estimation of system parameters and noise covariances of linear time-variant systems. Given measured data, this method maximizes the likelihood of the parameters. We solve the optimization problem of interest via a novel structure-exploiting solver. We present the advantages of the proposed approach over commonly used methods in the framework of Moving Horizon Estimation. Finally, we show the performance of the method through numerical simulations on a realistic example of a thermal system. In this example, the method can successfully estimate the model parameters in a short computational time.
56.
Roy, Wim Van; Nurkanovic, Armin; Abbasi-Esfeden, Ramin; Frey, Jonathan; Pozharskiy, Anton; Swevers, Jan; Diehl, Moritz
Continuous Optimization for Control of Finite-State Machines with Cascaded Hysteresis Via Time-Freezing Proceedings Article
In: 2023 62nd IEEE Conference on Decision and Control (CDC), pp. 6261-6266, IEEE, Singapore, Singapore, 2024, ISBN: 979-8-3503-0124-3.
@inproceedings{VanRoy2023CDC,
title = {Continuous Optimization for Control of Finite-State Machines with Cascaded Hysteresis Via Time-Freezing},
author = {Wim Van Roy and Armin Nurkanovic and Ramin Abbasi-Esfeden and Jonathan Frey and Anton Pozharskiy and Jan Swevers and Moritz Diehl},
doi = {10.1109/CDC49753.2023.10384083},
isbn = {979-8-3503-0124-3},
year = {2024},
date = {2024-01-19},
urldate = {2023-12-01},
booktitle = {2023 62nd IEEE Conference on Decision and Control (CDC)},
pages = {6261-6266},
publisher = {IEEE},
address = {Singapore, Singapore},
abstract = {Control problems with Finite-State Machines (FSM) are often solved using integer variables, leading to a mixed-integer optimal control problem (MIOCP). This paper proposes an alternative method to describe a subclass of FSMs using complementarity constraints and time-freezing. The FSM from this subclass is built up by a sequence of states where a transition between the states is triggered by a single switching function. This can be looked at as a cascade of hysteresis loops where a memory effect is used to maintain the active state of the state machine. Based on the reformulation for hybrid systems with a hysteresis loop [13], a method is developed to reformulate this subclass in a similar fashion. The approach transforms the original problem into a Piecewise Smooth System (PSS), which can be discretized using the recently developed Finite Elements with Switch Detection [15], allowing for high-accuracy solutions. The reformulation is compared to a mixed-integer formulation from the literature on a time-optimal control problem. This work is a first step towards the general reformulation of FSMs into nonsmooth systems without integer states.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Control problems with Finite-State Machines (FSM) are often solved using integer variables, leading to a mixed-integer optimal control problem (MIOCP). This paper proposes an alternative method to describe a subclass of FSMs using complementarity constraints and time-freezing. The FSM from this subclass is built up by a sequence of states where a transition between the states is triggered by a single switching function. This can be looked at as a cascade of hysteresis loops where a memory effect is used to maintain the active state of the state machine. Based on the reformulation for hybrid systems with a hysteresis loop [13], a method is developed to reformulate this subclass in a similar fashion. The approach transforms the original problem into a Piecewise Smooth System (PSS), which can be discretized using the recently developed Finite Elements with Switch Detection [15], allowing for high-accuracy solutions. The reformulation is compared to a mixed-integer formulation from the literature on a time-optimal control problem. This work is a first step towards the general reformulation of FSMs into nonsmooth systems without integer states.
57.
Bonassi, Fabio; Bella, Alessio La; Farina, Marcello; Scattolini, Riccardo
Nonlinear MPC design for incrementally ISS systems with application to GRU networks Journal Article
In: Automatica, vol. 159, iss. 11381, pp. 111381, 2024.
@article{bonassi2024nonlinear,
title = {Nonlinear MPC design for incrementally ISS systems with application to GRU networks},
author = {Fabio Bonassi and Alessio La Bella and Marcello Farina and Riccardo Scattolini},
doi = {https://doi.org/10.1016/j.automatica.2023.111381},
year = {2024},
date = {2024-01-03},
urldate = {2024-01-03},
journal = {Automatica},
volume = {159},
issue = {11381},
pages = {111381},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
58.
Kessler, Nicolas; Fagiano, Lorenzo
On the Design of Linear Time Varying Model Predictive Control for Trajectory Stabilization Working paper
2024.
@workingpaper{kessler2024lticontrol,
title = { On the Design of Linear Time Varying Model Predictive Control for Trajectory Stabilization},
author = {Nicolas Kessler and Lorenzo Fagiano },
year = {2024},
date = {2024-01-01},
abstract = {Stabilizing a reference trajectory of a nonlinear system is a recurrent, non-trivial task in control engineering. A common approach is to linearize the dynamics along the trajectory, thus deriving a linear-time-varying (LTV) model, and to design a model predictive controller (MPC), which results to be computationally efficient, since only convex programs need to be solved in real time, while retaining constraint handling capabilities. Building on recent developments in gain-scheduling control design,
where linearization errors and tracking error bounds are considered, a new approach to derive such LTV-MPC controllers is presented. The method addresses the systematic derivation of a suitable terminal cost. The resulting MPC law is tube-based, exploiting the co-designed auxiliary gain-scheduled controller.
Computational and implementation aspects are discussed as well, and the resulting hierarchical method is demonstrated both in simulation and in experiments with a small drone with fast dynamics and limited embedded computational capacity.},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
Stabilizing a reference trajectory of a nonlinear system is a recurrent, non-trivial task in control engineering. A common approach is to linearize the dynamics along the trajectory, thus deriving a linear-time-varying (LTV) model, and to design a model predictive controller (MPC), which results to be computationally efficient, since only convex programs need to be solved in real time, while retaining constraint handling capabilities. Building on recent developments in gain-scheduling control design,
where linearization errors and tracking error bounds are considered, a new approach to derive such LTV-MPC controllers is presented. The method addresses the systematic derivation of a suitable terminal cost. The resulting MPC law is tube-based, exploiting the co-designed auxiliary gain-scheduled controller.
Computational and implementation aspects are discussed as well, and the resulting hierarchical method is demonstrated both in simulation and in experiments with a small drone with fast dynamics and limited embedded computational capacity.
where linearization errors and tracking error bounds are considered, a new approach to derive such LTV-MPC controllers is presented. The method addresses the systematic derivation of a suitable terminal cost. The resulting MPC law is tube-based, exploiting the co-designed auxiliary gain-scheduled controller.
Computational and implementation aspects are discussed as well, and the resulting hierarchical method is demonstrated both in simulation and in experiments with a small drone with fast dynamics and limited embedded computational capacity.
59.
Bourkhissi, Lahcen El; Necoara, Ion
Complexity of linearized quadratic penalty for optimization with nonlinear equality constraints Working paper
2023, (Under review).
@workingpaper{bourkhissi2023complexity,
title = {Complexity of linearized quadratic penalty for optimization with nonlinear equality constraints},
author = {Lahcen El Bourkhissi and Ion Necoara},
doi = {https://doi.org/10.48550/arXiv.2402.15639},
year = {2023},
date = {2023-12-31},
abstract = {In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a linearized quadratic penalty method, i.e., we linearize the objective function and the functional constraints in the penalty formulation at the current iterate and add a quadratic regularization, thus yielding a subproblem that is easy to solve, and whose solution is the next iterate. Under a dynamic regularization parameter choice, we derive convergence guarantees for the iterates of our method to an ϵ first-order optimal solution in O(1/ϵ3) outer iterations. Finally, we show that when the problem data satisfy Kurdyka-Lojasiewicz property, e.g., are semialgebraic, the whole sequence generated by our algorithm converges and we derive convergence rates. We validate the theory and the performance of the proposed algorithm by numerically comparing it with the existing methods from the literature.},
note = {Under review},
keywords = {},
pubstate = {published},
tppubtype = {workingpaper}
}
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a linearized quadratic penalty method, i.e., we linearize the objective function and the functional constraints in the penalty formulation at the current iterate and add a quadratic regularization, thus yielding a subproblem that is easy to solve, and whose solution is the next iterate. Under a dynamic regularization parameter choice, we derive convergence guarantees for the iterates of our method to an ϵ first-order optimal solution in O(1/ϵ3) outer iterations. Finally, we show that when the problem data satisfy Kurdyka-Lojasiewicz property, e.g., are semialgebraic, the whole sequence generated by our algorithm converges and we derive convergence rates. We validate the theory and the performance of the proposed algorithm by numerically comparing it with the existing methods from the literature.
60.
Bourkhissi, Lahcen El; Necoara, Ion; Patrinos, Panagiotis
Linearized ADMM for Nonsmooth Nonconvex Optimization with Nonlinear Equality Constraints Proceedings Article
In: 2023 62nd IEEE Conference on Decision and Control (CDC), pp. 7312-7317, IEEE, Singapore, Singapore, 2023, ISSN: 2576-2370.
@inproceedings{Lahcen23LinADMM,
title = {Linearized ADMM for Nonsmooth Nonconvex Optimization with Nonlinear Equality Constraints},
author = {Lahcen El Bourkhissi and Ion Necoara and Panagiotis Patrinos},
doi = {10.1109/CDC49753.2023.10384166},
issn = {2576-2370},
year = {2023},
date = {2023-12-13},
urldate = {2023-12-13},
booktitle = {2023 62nd IEEE Conference on Decision and Control (CDC)},
pages = {7312-7317},
publisher = {IEEE},
address = {Singapore, Singapore},
abstract = {This paper proposes a new approach for solving a structured nonsmooth nonconvex optimization problem with nonlinear equality constraints, where both the objective function and constraints are 2-blocks separable. Our method is based on a 2-block linearized ADMM, where we linearize the smooth part of the cost function and the nonlinear term of the functional constraints in the augmented Lagrangian at each outer iteration. This results in simple subproblems, whose solutions are used to update the iterates of the 2 blocks variables. We prove global convergence for the sequence generated by our method to a stationary point of the original problem. To demonstrate its effectiveness, we apply our proposed algorithm as a solver for the nonlinear model predictive control problem of an inverted pendulum on a cart.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
This paper proposes a new approach for solving a structured nonsmooth nonconvex optimization problem with nonlinear equality constraints, where both the objective function and constraints are 2-blocks separable. Our method is based on a 2-block linearized ADMM, where we linearize the smooth part of the cost function and the nonlinear term of the functional constraints in the augmented Lagrangian at each outer iteration. This results in simple subproblems, whose solutions are used to update the iterates of the 2 blocks variables. We prove global convergence for the sequence generated by our method to a stationary point of the original problem. To demonstrate its effectiveness, we apply our proposed algorithm as a solver for the nonlinear model predictive control problem of an inverted pendulum on a cart.