Reinforcement Learning for Fuzzy Structured Adaptive Optimal Control of Discrete-Time Nonlinear Complex Networks

This article focuses on fuzzy structural adaptive optimal control issue of discrete-time nonlinear complex networks (CNs) via adopting the reinforcement learning (RL) and Takagi-Sugeno fuzzy modeling approaches, where the control gains are subjected to structured constraints. In accordance with the Bellman optimality theory, the modified fuzzy coupled algebraic Riccati equations (CAREs) are constructed for discrete-time fuzzy CNs, while the modified fuzzy CAREs are difficult to solve directly through mathematical approaches. Then, a model-based offline learning iteration algorithm is developed to solve the modified fuzzy CAREs, where the network dynamics information is needed. Moreover, a novel data-driven off-policy RL algorithm is given to compute the modified fuzzy CAREs, and the structural optimal solutions can be obtained directly by using the collected state and input data in the absence of the network dynamics information. Furthermore, the convergence proofs of the presented learning algorithms are provided. In the end, the validity and practicability of the theoretical results are explicated via two numerical simulations.