ADP-Based Decentralized Controller Design for Nonlinear Time-Delay Interconnected Systems

The control of industrial processes which can be generally described by nonlinear time-delay interconnected systems is very important. A decentralized control method based on adaptive dynamic programming (ADP) is proposed in this article, which can solve the control and stability problem for nonlinear time-delay interconnected systems using past state data and interconnection information. First, the form of nonlinear interconnected systems with state delay is given. Based on such systems, the subsystems are reconstructed by adding the upper bound of the interconnection part to the cost function. New cost functions are constructed which include a series of Hamilton-Jacobi–Bellman (HJB) equations with Lyapunov-Krasovskii (L-K) function, where the past state data and interconnection information are employed. Then, the control problem can be dealt with by solving the HJB equations. The HJB equations can be solved by the critic learning method based on ADP, where the critic neural networks (NNs) are applied to estimate the optimal cost function. The weights can be calculated by the gradient descent method, and the control law can be obtained. Subsequently, the stability of the closed-loop system is proved in the sense of uniformly ultimately bounded (UUB). Finally, simulation results verify the effectiveness of the proposed method by a nonlinear time-delay interconnected system and two-stage chemical reactors.