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

• Published in: IEEE transactions on cybernetics Vol. 52; no. 2; pp. 1048 - 1060
• Main Authors: Rizvi, Syed Ali Asad, Lin, Zongli
• Format: Journal Article
• Language: English
• 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
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2020.2989419

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.