H ∞ Control Synthesis for Linear Parabolic PDE Systems with Model-Free Policy Iteration

The H∞ control problem is considered for linear parabolic partial differential equation PDE systems with completely unknown system dynamics. We propose a model-free policy iteration PI method for learning the H∞ control policy by using measured system data without system model information. First, a finite-dimensional system of ordinary differential equation ODE is derived, which accurately describes the dominant dynamics of the parabolic PDE system. Based on the finite-dimensional ODE model, the H∞ control problem is reformulated, which is theoretically equivalent to solving an algebraic Riccati equation ARE. To solve the ARE without system model information, we propose a least-square based model-free PI approach by using real system data. Finally, the simulation results demonstrate the effectiveness of the developed model-free PI method.