A Safety-Certified Policy Iteration Algorithm for Control of Constrained Nonlinear Systems

Yazdani, Navid Moshtaghi; Moghaddam, Reihaneh Kardehi; Kiumarsi, Bahare; Modares, Hamidreza

doi:10.1109/lcsys.2020.2990632

Cited by 13 publications

(6 citation statements)

References 30 publications

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“…Moreover, for the existing safe-certified ADP method with CBF [26], [48], the admissible control space based on CBF should be added as the extra constraint into the optimal control problem, and this kind of constraint is associated with model information closely. Both of these factors will bring extra computation burden in the process of solving the specific optimization problem.…”

Section: B Safe Constraints Handlingmentioning

confidence: 99%

ADP-Based Optimal Control for Discrete-Time Systems With Safe Constraints and Disturbances

Ye,

Dong,

Bian

et al. 2024

IEEE Trans. Automat. Sci. Eng.

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Section: B Safe Constraints Handlingmentioning

confidence: 99%

ADP-Based Optimal Control for Discrete-Time Systems With Safe Constraints and Disturbances

Ye,

Dong,

Bian

et al. 2024

IEEE Trans. Automat. Sci. Eng.

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“…The presence of an optimal stabilizing solution is ensured under mild assumptions about the reward function and system dynamics [26] .…”

Section: Optimal Control Of Dynamical Systemsmentioning

confidence: 99%

“…Theorem 1. Theorem 10.1.2 [26] considers system (1) with performance function ( 2), there must be a positive semi-definite function ( )…”

Section: Optimal Control Of Dynamical Systemsmentioning

confidence: 99%

Safety-critical Policy Iteration Algorithm for Control under Model Uncertainty

Yazdani

Moghaddam

Olyaei

2022

artif. intell. adv.

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Safety is an important aim in designing safe-critical systems. To design such systems, many policy iterative algorithms are introduced to find safe optimal controllers. Due to the fact that in most practical systems, finding accurate information from the system is rather impossible, a new online training method is presented in this paper to perform an iterative reinforcement learning based algorithm using real data instead of identifying system dynamics. Also, in this paper the impact of model uncertainty is examined on control Lyapunov functions (CLF) and control barrier functions (CBF) dynamic limitations. The Sum of Square program is used to iteratively find an optimal safe control solution. The simulation results which are applied on a quarter car model show the efficiency of the proposed method in the fields of optimality and robustness.

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“…In [25], it has been shown that one can efficiently relax the Bellman equation to an SOS optimization problem. Many of other problems in control theory, such as optimal control of discrete‐time systems [26], H ∞ control of polynomial [27], polynomial fuzzy [28], and uncertain polynomial systems [29], mixed H 2 / H ∞ control design [30], H ∞ control of polynomial systems with adjustable parameters ( H ∞ codesign) [31], multi‐objective control design [32], and constrained states control [33], have been solved with the idea of SOS‐based ADP.…”

Section: Introductionmentioning

confidence: 99%

Policy iteration forH_∞control of polynomial time‐varying systems

Pakkhesal,

Shamaghdari

2024

IET Control Theory & Appl

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This paper studies the H∞ control problem for polynomial time‐varying systems. The H∞ control problem has been much less investigated for time‐varying systems in comparison to the time‐invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time‐varying H∞ control problem with the ADP approach. Considering the time as an independent variable for sum‐of‐squares (SOS) optimization problems, an SOS‐based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed‐loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H∞ controller with a smaller disturbance attenuation coefficient, a two‐loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples.

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A Safety-Certified Policy Iteration Algorithm for Control of Constrained Nonlinear Systems

Cited by 13 publications

References 30 publications

ADP-Based Optimal Control for Discrete-Time Systems With Safe Constraints and Disturbances

ADP-Based Optimal Control for Discrete-Time Systems With Safe Constraints and Disturbances

Safety-critical Policy Iteration Algorithm for Control under Model Uncertainty

Policy iteration forH_∞control of polynomial time‐varying systems

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A Safety-Certified Policy Iteration Algorithm for Control of Constrained Nonlinear Systems

Cited by 13 publications

References 30 publications

ADP-Based Optimal Control for Discrete-Time Systems With Safe Constraints and Disturbances

ADP-Based Optimal Control for Discrete-Time Systems With Safe Constraints and Disturbances

Safety-critical Policy Iteration Algorithm for Control under Model Uncertainty

Policy iteration forH∞control of polynomial time‐varying systems

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Product

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Policy iteration forH_∞control of polynomial time‐varying systems