Data-Driven Nonlinear Optimal Control for Distributed Parameter Systems with Output Delay

摘要

This paper presents a predictive nonlinear optimal control method for nonlinear distributed parameter systems with output delay by means of a data-driven modeling method called the dynamic mode decomposition. Nonlinear optimal control problems can be solved by an exact numerical solver of Hamilton-Jacobi equations called the stable manifold method. A nonlinear optimal control for distributed parameter systems has been proposed in terms of a finite-dimensional reduction derived from time series data of system responses. The optimal controllers consist of optimal gains at each state on an optimal orbit. Thus, output delays bring on the mismatch between gains calculated from observations and actual states of controlled systems. A state prediction realized by the dynamic mode decomposition can recover a performance degradation arisen from the delay.