Integral reinforcement learning‐based optimal tracking control for uncertain nonlinear systems under input constraint and specified performance constraints

• Published in: International journal of robust and nonlinear control Vol. 34; no. 13; pp. 8802 - 8824
• Main Authors: Chang, Ru, Liu, Zhi‐Meng, Li, Xiao‐Bin, Sun, Chang‐Yin
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.09.2024
• Subjects: Algorithms; Constraints; Control systems; Cost function; Disturbances; Error analysis; Game theory; input constraint; Machine learning; Neural networks; Nonlinear control; Nonlinear systems; Optimal control; optimal tracking control; prescribed performance control; reinforcement learning; System dynamics; Tracking control; Tracking errors; uncertain nonlinear systems; zero‐sum game
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7415

This article addresses the optimal tracking control problem with prescribed performance for uncertain nonlinear systems subject to input constraint and unknown disturbances. First, a fixed‐time monotonic convergence function is introduced to restrain tracking error, and a nonlinear mapping technique is employed to transform the constrained error into an unconstrained variable, then the fixed‐time output tracking issue is boiled down to the boundedness problem of the transformed variable. With the aid of a nonquadratic cost function, the input constraint is encoded into the optimization problem. To solve the unknown disturbances, an auxiliary system and an auxiliary disturbance policy are constructed, and the optimal control problem is formulated as a two‐player zero‐sum game. Moreover, a Hamilton–Jacobi–Isaacs (HJI) equation associated with this nonquadratic zero‐sum game is established to give the optimal control and the worst‐case disturbance policy solution. Subsequently, to avoid using knowledge of the system dynamics, three neural network approximators, namely, actor, critic, and disturbance, which are tuned online and simultaneously for approximating the solution of HJI, are constructed based on the integral reinforcement learning algorithm. Theoretical analysis shows that the reconstructed error system states and the weight estimation errors are semi‐globally uniformly ultimately bounded. Finally, the simulation study further tests the availability of the proposed control strategy.