Infinite horizon optimal control of a class of nonlinear systems

In Banks et al. (1992) it is shown that for the class of nonlinear systems x˙=A(x)xi-B(x)u, the solution of the infinite horizon optimal control problem leads to a state dependent Riccati equation. These results may be employed to generate stabilizing and optimal control laws in a manner which closely parallels the linear quadratic (LQ) technique commonly applied to linear dynamical systems. In the present work we apply this result to a more general class of nonlinear systems, in the form x˙=f(x)-g(x)u, by means of an appropriate transformation. We also study the robustness and implementability of this technique in real time control applications. Experimental results are given for the nonlinear benchmark problem introduced in Kokotovic et al. (1991). Similar to the linear quadratic (LQ) technique, we obtain time-domain responses which are easily and transparently tuned by adjusting the entries in the penalty matrices