ON THE NONLINEAR OPTIMAL REGULATOR PROBLEM

The linear quadratic regulator is one of the most widely used tools for control systems design. Many real world systems, however, are inherently nonlinear and can only be optimally regulated using a nonlinear controller. This is, in general, much more difficult to achieve than the linear quadratic case. In this paper we show that a nonlinear feedback controller can be synthesized by appropriate training of a feedforward neural network to satisfy the corresponding nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equation in a restricted domain of the state space. Asymptotic stability of the closed-loop system is shown to be a natural consequence of the HJB equation.