Stabilization and Stochastic Control of a Class of Nonlinear Systems.

摘要

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. Composite control originally proposed in a deterministic context is generalized to the problem with white noise inputs. However, the approach used here is radically different from the deterministic approach. Presence of noise smoothed the system behavior and allowed a more complete solution than in the deterministic case. (Author)