Proper orthogonal decomposition based feedback optimal control synthesis of distributed parameter systems using neural networks

A new method for optimal control design of distributed parameter systems is presented in this paper. The concept of proper orthogonal decomposition is used for the model reduction of distributed parameter systems to form a reduced order lumped parameter problem. The optimal control problem is then solved in the time domain, in a state feedback sense, following the philosophy of 'adaptive critic' neural networks. The control solution is then mapped back to the spatial domain using the same basis functions. Numerical simulation results are presented for a linear and nonlinear one-dimensional heat equation problem in an infinite time regulator framework.