Adaptive dynamic programming for self-triggered optimal control in industrial spatiotemporal processes

Industrial spatiotemporal processes are characterized by highly-dissipative partial differential equations (HPDE) with infinite dimensionality, nonlinearity, and strong spatiotemporal coupling. Precise control of such processes is critical for enhancing material quality and consistency. Since frequent updates of control inputs can easily lead to instability in state distributions, this paper investigates an adaptive self-triggered driven optimal control method for the HPDE. By dynamically predicting triggered instants, this method effectively overcomes the limitations associated with the continuous monitoring required by most existing triggered conditions. First, the self-triggered control problem of HPDE is formulated and transformed into the solution of the Hamilton-Jacobi-Bellman equation. A novel self-triggered mechanism for the HPDE system is further investigated and designed by integrating the HPDE states, control information, and Lyapunov stability analysis. Subsequently, by leveraging the formidable approximation capabilities of neural networks, adaptive dynamic programming is empowered to effectively estimate the optimal value function, thereby deriving the self-triggered optimal control. The boundedness of the self-triggered intervals and performance, and the stability of the closed-loop system are theoretically analyzed and discussed. Finally, the proposed method is applied to a typical industrial spatiotemporal process to verify its convergence, stability, and effectiveness.