Publications
41.
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}
}
42.
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}
}
43.
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}
}
44.
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.
45.
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.
46.
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.
47.
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.
48.
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.}
49.
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}
}
50.
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.
51.
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.
52.
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}
}
53.
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.
54.
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.
55.
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.
56.
Kessler, Nicolas; Fagiano, Lorenzo
On the stabilization of forking and cyclic trajectories for nonlinear systems Proceedings Article
In: 3rd Modeling, Estimation and Control Conference MECC 2023, pp. 199–204, IFAC-PapersOnLine, Lake Tahoe, NV, USA, 2023, ISSN: 2405-8963.
@inproceedings{kessler2023stabilization,
title = {On the stabilization of forking and cyclic trajectories for nonlinear systems},
author = {Nicolas Kessler and Lorenzo Fagiano },
url = {https://www.sciencedirect.com/science/article/pii/S2405896323023571},
doi = {https://doi.org/10.1016/j.ifacol.2023.12.024},
issn = {2405-8963},
year = {2023},
date = {2023-12-03},
urldate = {2023-12-03},
booktitle = {3rd Modeling, Estimation and Control Conference MECC 2023},
volume = {56},
number = {3},
pages = {199--204},
publisher = {IFAC-PapersOnLine},
address = {Lake Tahoe, NV, USA},
abstract = {Stabilizing a reference trajectory for a nonlinear system is a common, non-trivial task in control theory. An approach to solve this problem is to approximate the nonlinear system along the trajectory as an uncertain linear time-varying one, and to solve an optimization problem featuring Linear Matrix Inequality (LMI) constraints to derive a stabilizing, smooth, gain-scheduled control law. Such an approach is extended here by considering a set of reference trajectories instead of a single one, such that switching among them is permitted. These switching events are commonly encountered in industrial plants, such as energy generation systems, and are of high relevance in practice. The approach allows one to derive a gain-scheduled control law guaranteeing asymptotic stability also during the switching and accounting for the linearization errors. Simulation results on a chemical system highlight the effectiveness of the method.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Stabilizing a reference trajectory for a nonlinear system is a common, non-trivial task in control theory. An approach to solve this problem is to approximate the nonlinear system along the trajectory as an uncertain linear time-varying one, and to solve an optimization problem featuring Linear Matrix Inequality (LMI) constraints to derive a stabilizing, smooth, gain-scheduled control law. Such an approach is extended here by considering a set of reference trajectories instead of a single one, such that switching among them is permitted. These switching events are commonly encountered in industrial plants, such as energy generation systems, and are of high relevance in practice. The approach allows one to derive a gain-scheduled control law guaranteeing asymptotic stability also during the switching and accounting for the linearization errors. Simulation results on a chemical system highlight the effectiveness of the method.
57.
Voogd, Kevin; Allamaa, Jean Pierre; Alonso-Mora, Javier; Son, Tong Duy
Reinforcement Learning from Simulation to Real World Autonomous Driving using Digital Twin Proceedings Article
In: 22nd IFAC World Congress 2023, pp. 1510-1515, Elsevier Ltd, Yokohama, Japan, 2023, ISSN: 2405-8963.
@inproceedings{Voogd2023ReinforcementLF,
title = {Reinforcement Learning from Simulation to Real World Autonomous Driving using Digital Twin},
author = {Kevin Voogd and Jean Pierre Allamaa and Javier Alonso-Mora and Tong Duy Son},
url = {https://www.sciencedirect.com/science/article/pii/S2405896323022553},
doi = {https://doi.org/10.1016/j.ifacol.2023.10.1846},
issn = {2405-8963},
year = {2023},
date = {2023-11-30},
urldate = {2023-11-30},
booktitle = {22nd IFAC World Congress 2023},
journal = {IFAC-PapersOnLine},
volume = {56},
number = {2},
pages = {1510-1515},
publisher = {Elsevier Ltd},
address = {Yokohama, Japan},
abstract = {Reinforcement learning (RL) is a promising solution for autonomous vehicles to deal with complex and uncertain traffic environments. The RL training process is however expensive, unsafe, and time-consuming. Algorithms are often developed first in simulation and then transferred to the real-world, leading to a common sim2real challenge where performance decreases when the domain changes. In this paper, we propose a transfer learning process to minimize the gap by exploiting digital twin technology, relying on a systematic and simultaneous combination of virtual and real world data coming from vehicle dynamics and traffic scenarios. The model and testing environment is evolved from model, hardware to vehicle in the loop and proving ground testing stages, similar to standard development cycle in the automotive industry. In particular, we also integrate other transfer learning techniques such as domain randomization and adaptation in each stage. The simulation and real data are gradually incorporated to accelerate and make the transfer learning process more robust. The proposed RL methodology is applied to develop a path-following steering controller for an autonomous electric vehicle. After learning and deploying the real-time RL control policy on the vehicle, we obtained satisfactory and safe control performance already from the first deployment, demonstrating the advantages of the proposed digital twin based learning process.
},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Reinforcement learning (RL) is a promising solution for autonomous vehicles to deal with complex and uncertain traffic environments. The RL training process is however expensive, unsafe, and time-consuming. Algorithms are often developed first in simulation and then transferred to the real-world, leading to a common sim2real challenge where performance decreases when the domain changes. In this paper, we propose a transfer learning process to minimize the gap by exploiting digital twin technology, relying on a systematic and simultaneous combination of virtual and real world data coming from vehicle dynamics and traffic scenarios. The model and testing environment is evolved from model, hardware to vehicle in the loop and proving ground testing stages, similar to standard development cycle in the automotive industry. In particular, we also integrate other transfer learning techniques such as domain randomization and adaptation in each stage. The simulation and real data are gradually incorporated to accelerate and make the transfer learning process more robust. The proposed RL methodology is applied to develop a path-following steering controller for an autonomous electric vehicle. After learning and deploying the real-time RL control policy on the vehicle, we obtained satisfactory and safe control performance already from the first deployment, demonstrating the advantages of the proposed digital twin based learning process.
58.
Acerbo, Flavia Sofia; Swevers, Jan; Tuytelaars, Tinne; Son, Tong Duy
Evaluation of MPC-based Imitation Learning for Human-like Autonomous Driving Proceedings Article
In: 22nd IFAC World Congress, pp. 4871-4876, Elsevier Ltd, Yokohama, Japan, 2023, ISSN: 2405-8963.
@inproceedings{acerboEvaluationMPCbasedImitation2023,
title = {Evaluation of MPC-based Imitation Learning for Human-like Autonomous Driving},
author = {Flavia Sofia Acerbo and Jan Swevers and Tinne Tuytelaars and Tong Duy Son},
url = {https://www.sciencedirect.com/science/article/pii/S2405896323016610},
doi = {https://doi.org/10.1016/j.ifacol.2023.10.1257},
issn = {2405-8963},
year = {2023},
date = {2023-11-30},
urldate = {2023-11-30},
booktitle = {22nd IFAC World Congress},
journal = { IFAC-PapersOnLine},
volume = {56},
number = {2},
pages = {4871-4876},
publisher = {Elsevier Ltd},
address = {Yokohama, Japan},
abstract = {This work evaluates and analyzes the combination of imitation learning (IL) and differentiable model predictive control (MPC) for the application of human-like autonomous driving. We combine MPC with a hierarchical learning-based policy, and measure its performance in open-loop and closed-loop with metrics related to safety, comfort and similarity to human driving characteristics. We also demonstrate the value of augmenting open-loop behavioral cloning with closed-loop training for a more robust learning, approximating the policy gradient through time with the state space model used by the MPC. We perform experimental evaluations on a lane keeping control system, learned from demonstrations collected on a fixed-base driving simulator, and show that our imitative policies approach the human driving style preferences.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
This work evaluates and analyzes the combination of imitation learning (IL) and differentiable model predictive control (MPC) for the application of human-like autonomous driving. We combine MPC with a hierarchical learning-based policy, and measure its performance in open-loop and closed-loop with metrics related to safety, comfort and similarity to human driving characteristics. We also demonstrate the value of augmenting open-loop behavioral cloning with closed-loop training for a more robust learning, approximating the policy gradient through time with the state space model used by the MPC. We perform experimental evaluations on a lane keeping control system, learned from demonstrations collected on a fixed-base driving simulator, and show that our imitative policies approach the human driving style preferences.
59.
Reiter, Rudolf; Nurkanovic, Armin; Frey, Jonathan; Diehl, Moritz
Frenet-Cartesian model representations for automotive obstacle avoidance within nonlinear MPC Journal Article
In: European Journal of Control, vol. 74, pp. 100847, 2023, ISSN: 0947-3580, (2023 European Control Conference Special Issue).
@article{REITER2023100847,
title = {Frenet-Cartesian model representations for automotive obstacle avoidance within nonlinear MPC},
author = {Rudolf Reiter and Armin Nurkanovic and Jonathan Frey and Moritz Diehl},
url = {https://www.sciencedirect.com/science/article/pii/S0947358023000766},
doi = {https://doi.org/10.1016/j.ejcon.2023.100847},
issn = {0947-3580},
year = {2023},
date = {2023-11-01},
journal = {European Journal of Control},
volume = {74},
pages = {100847},
abstract = {In recent years, nonlinear model predictive control has been extensively used for solving automotive motion control and planning tasks. In order to formulate the nonlinear model predictive control problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the nonlinear MPC related optimization problem, involving a Cartesian and a Frenet coordinate frame in a single nonlinear program. We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints. With this approach, we exploit the simpler formulation of opponent vehicle constraints in the Cartesian coordinate frame, as well as road-aligned costs and constraints related to the Frenet coordinate frame. Comparisons to other approaches in a simulation framework highlight the advantages of the proposed methods.},
note = {2023 European Control Conference Special Issue},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In recent years, nonlinear model predictive control has been extensively used for solving automotive motion control and planning tasks. In order to formulate the nonlinear model predictive control problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the nonlinear MPC related optimization problem, involving a Cartesian and a Frenet coordinate frame in a single nonlinear program. We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints. With this approach, we exploit the simpler formulation of opponent vehicle constraints in the Cartesian coordinate frame, as well as road-aligned costs and constraints related to the Frenet coordinate frame. Comparisons to other approaches in a simulation framework highlight the advantages of the proposed methods.
60.
Zhang, Yuan; Wang, Jianhong; Boedecker, Joschka
Robust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization Proceedings Article
In: 7th Annual Conference on Robot Learning, 2023.
@inproceedings{zhang2023robust,
title = {Robust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization},
author = {Yuan Zhang and Jianhong Wang and Joschka Boedecker},
url = {https://openreview.net/forum?id=keAPCON4jHC},
year = {2023},
date = {2023-10-16},
urldate = {2023-10-16},
booktitle = {7th Annual Conference on Robot Learning},
abstract = {Reinforcement learning (RL) is recognized as lacking generalization and robustness under environmental perturbations, which excessively restricts its application for real-world robotics. Prior work claimed that adding regularization to the value function is equivalent to learning a robust policy under uncertain transitions. Although the regularization-robustness transformation is appealing for its simplicity and efficiency, it is still lacking in continuous control tasks. In this paper, we propose a new regularizer named Uncertainty Set Regularizer (USR), to formulate the uncertainty set on the parametric space of a transition function. To deal with unknown uncertainty sets, we further propose a novel adversarial approach to generate them based on the value function. We evaluate USR on the Real-world Reinforcement Learning (RWRL) benchmark and the Unitree A1 Robot, demonstrating improvements in the robust performance of perturbed testing environments and sim-to-real scenarios.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Reinforcement learning (RL) is recognized as lacking generalization and robustness under environmental perturbations, which excessively restricts its application for real-world robotics. Prior work claimed that adding regularization to the value function is equivalent to learning a robust policy under uncertain transitions. Although the regularization-robustness transformation is appealing for its simplicity and efficiency, it is still lacking in continuous control tasks. In this paper, we propose a new regularizer named Uncertainty Set Regularizer (USR), to formulate the uncertainty set on the parametric space of a transition function. To deal with unknown uncertainty sets, we further propose a novel adversarial approach to generate them based on the value function. We evaluate USR on the Real-world Reinforcement Learning (RWRL) benchmark and the Unitree A1 Robot, demonstrating improvements in the robust performance of perturbed testing environments and sim-to-real scenarios.