Adaptive Dynamic Programming for Model-Free Global Stabilization of Control Constrained Continuous-Time Systems

This article addresses the problem of global stabilization of continuous-time linear systems subject to control constraints using a model-free approach. We propose a gain-scheduled low-gain feedback scheme that prevents saturation from occurring and achieves global stabilization. The framework of pa...

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Published inIEEE transactions on cybernetics Vol. 52; no. 2; pp. 1048 - 1060
Main Authors Rizvi, Syed Ali Asad, Lin, Zongli
Format Journal Article
LanguageEnglish
Published United States IEEE 01.02.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Actuator saturation
Actuators
Adaptive control
adaptive dynamic programming (ADP)
Algorithms
Asymptotic stability
constrained control
Constraint modelling
Continuous time systems
Control theory
Dynamic programming
Feedback control
iterative learning
Iterative methods
Linear systems
Mathematical model
Output feedback
Parameterization
Riccati equation
Riccati equations
Stability analysis
Stabilization
State feedback
System dynamics
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Abstract This article addresses the problem of global stabilization of continuous-time linear systems subject to control constraints using a model-free approach. We propose a gain-scheduled low-gain feedback scheme that prevents saturation from occurring and achieves global stabilization. The framework of parameterized algebraic Riccati equations (AREs) is employed to design the low-gain feedback control laws. An adaptive dynamic programming (ADP) method is presented to find the solution of the parameterized ARE without requiring the knowledge of the system dynamics. In particular, we present an iterative ADP algorithm that searches for an appropriate value of the low-gain parameter and iteratively solves the parameterized ADP Bellman equation. We present both state feedback and output feedback algorithms. The closed-loop stability and the convergence of the algorithm to the nominal solution of the parameterized ARE are shown. The simulation results validate the effectiveness of the proposed scheme.
AbstractList This article addresses the problem of global stabilization of continuous-time linear systems subject to control constraints using a model-free approach. We propose a gain-scheduled low-gain feedback scheme that prevents saturation from occurring and achieves global stabilization. The framework of parameterized algebraic Riccati equations (AREs) is employed to design the low-gain feedback control laws. An adaptive dynamic programming (ADP) method is presented to find the solution of the parameterized ARE without requiring the knowledge of the system dynamics. In particular, we present an iterative ADP algorithm that searches for an appropriate value of the low-gain parameter and iteratively solves the parameterized ADP Bellman equation. We present both state feedback and output feedback algorithms. The closed-loop stability and the convergence of the algorithm to the nominal solution of the parameterized ARE are shown. The simulation results validate the effectiveness of the proposed scheme.
This article addresses the problem of global stabilization of continuous-time linear systems subject to control constraints using a model-free approach. We propose a gain-scheduled low-gain feedback scheme that prevents saturation from occurring and achieves global stabilization. The framework of parameterized algebraic Riccati equations (AREs) is employed to design the low-gain feedback control laws. An adaptive dynamic programming (ADP) method is presented to find the solution of the parameterized ARE without requiring the knowledge of the system dynamics. In particular, we present an iterative ADP algorithm that searches for an appropriate value of the low-gain parameter and iteratively solves the parameterized ADP Bellman equation. We present both state feedback and output feedback algorithms. The closed-loop stability and the convergence of the algorithm to the nominal solution of the parameterized ARE are shown. The simulation results validate the effectiveness of the proposed scheme.This article addresses the problem of global stabilization of continuous-time linear systems subject to control constraints using a model-free approach. We propose a gain-scheduled low-gain feedback scheme that prevents saturation from occurring and achieves global stabilization. The framework of parameterized algebraic Riccati equations (AREs) is employed to design the low-gain feedback control laws. An adaptive dynamic programming (ADP) method is presented to find the solution of the parameterized ARE without requiring the knowledge of the system dynamics. In particular, we present an iterative ADP algorithm that searches for an appropriate value of the low-gain parameter and iteratively solves the parameterized ADP Bellman equation. We present both state feedback and output feedback algorithms. The closed-loop stability and the convergence of the algorithm to the nominal solution of the parameterized ARE are shown. The simulation results validate the effectiveness of the proposed scheme.
Author Rizvi, Syed Ali Asad
Lin, Zongli
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SubjectTerms Actuator saturation
Actuators
Adaptive control
adaptive dynamic programming (ADP)
Algorithms
Asymptotic stability
constrained control
Constraint modelling
Continuous time systems
Control theory
Dynamic programming
Feedback control
iterative learning
Iterative methods
Linear systems
Mathematical model
Output feedback
Parameterization
Riccati equation
Riccati equations
Stability analysis
Stabilization
State feedback
System dynamics
Title Adaptive Dynamic Programming for Model-Free Global Stabilization of Control Constrained Continuous-Time Systems
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