ABSTRACT
JAGAN: “dk3189_c009” — 2006/3/13 — 11:47 — page 473 — #1
In the literature, there are many methods of designing stable controllers for nonlinear systems. However, stability is only a bare minimum requirement in a system design. Previous chapters discuss the design of controllers for various classes of nonlinear discrete-time systems using neural networks (NNs). Ensuring optimality guarantees the stability of the nonlinear system; however, optimal control of nonlinear systems is a difficult and challenging area. If the system is modeled by linear dynamics and the cost functional to be minimized is quadratic in state and control, then optimal control is a linear feedback of states, where the gains are obtained by solving a standard Riccati equation (Lewis 1992). On the other hand, if the system is modeled by nonlinear dynamics or the cost functional is nonquadratic, the optimal state feedback control will depend upon obtaining the solution to the Hamilton-Jacobi-Bellman (HJB) equation (Saridis and Lee 1979), which is generally nonlinear. The HJB equation is difficult to solve directly because it involves solving either nonlinear partial difference equations or nonlinear partial differential equations.
