Safe adaptive learning algorithm with neural network implementation for H∞ control of nonlinear safety‐critical system

• Published in: International journal of robust and nonlinear control Vol. 33; no. 1; pp. 372 - 391
• Main Authors: Qin, Chunbin, Wang, Jinguang, Zhu, Heyang, Xiao, Qiyang, Zhang, Dehua
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.01.2023
• Subjects: Adaptive algorithms; Adaptive control; adaptive dynamic programming; Adaptive learning; barrier function; Constraints; Damping; Dynamic programming; H-infinity control; H∞$$ {H}_{\infty } $$ control; Machine learning; neural network; Neural networks; Nonlinear control; Parameters; Safety; safety‐critical system
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6452

In this article, the H∞$$ {H}_{\infty } $$ safe control problem of continuous‐time affine nonlinear safety‐critical systems is studied based on the barrier function (BF) and adaptive dynamic programming (ADP). We show that the safety constraints in this article occur under the condition that the system initial state is unsafe and have not been adequately addressed in the existing work. First, the H∞$$ {H}_{\infty } $$ control problem is transformed into a zero‐sum game problem, and a new safe Hamilton–Jacobi–Isaacs equation is proposed by combining with the BF, which makes the unsafe behavior be punished in the learning process. In addition, a damping coefficient is introduced into the BF to punish the unsafe behavior more flexibly. Aiming at the requirement that the initial system state must be strictly constrained in the safe set, a new weight updating method based on ADP is proposed, which can reasonably avoid the influence of the BF on neural network (NN) parameters when the initial system state is unsafe. Furthermore, based on the Lyapunov stability theory, it is proved that the system states of safety‐critical systems and the NN parameters are uniformly ultimately bounded under the safety constraints and disturbances effect. Finally, the effectiveness of the proposed method is verified by two simulation examples.