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

Abstract

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.