Adaptive critic design-based robust neural network control for nonlinear distributed parameter systems with unknown dynamics

In this paper, an adaptive critic design (ACD)-based robust on-line neural network control design is developed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinear dynamics. First, the Galerkin method is applied to the parabolic PDE system to derive a finite-dimensional slow one and an infinite-dimensional stable fast subsystem. The obtained slow system is an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the slow modes of the PDE system. Then, a novel ACD-based robust optimal control scheme is proposed for the resulting nonlinear slow system with unknown dynamics. An action neural network (NN) is employed to approximate all the derived unknown nonlinear terms and a robust control term is further developed to attenuate the NN reconstruction errors and disturbances. Especially, by developing novel critic signals and Lyapunov function candidate, together with the adaptive bounding technique, no a prior knowledge for the bounds of the disturbance term, the NN ideal weights of action NN and critic NN and the NN reconstruction errors is required. Finally, simulation results demonstrate the effectiveness of the proposed robust optimal control scheme.