A two-stage Lyapunov-Bellman feedback design of a class of nonlinear systems

The composite control proposed in an earlier paper for a class of singularly perturbed nonlinear systems is now shown to possess properties essential for near-optimal feedback design. It asymptotically stabilizes the desired equilibrium and produces a finite cost which tends to the optimal cost for a slow problem as the singular perturbation parameter tends to zero. Thus, the well-posedness of the full regulator problem is established. The stability results are also applicable to two-time-scale systems which are not singularly perturbed, and the paper does not assume the knowledge of singular perturbation techniques.