Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems

• Published in: IEEE transaction on neural networks and learning systems Vol. 26; no. 11; pp. 2949 - 2961
• Main Authors: Luo, Biao, Huang, Tingwen, Wu, Huai-Ning, Yang, Xiong
• Format: Journal Article
• Language: English
• Published: United States 01.11.2015
• ISSN: 2162-2388
• DOI: 10.1109/TNNLS.2015.2461023

The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.