An optimal feedback regulation of nonlinear singularly perturbed systems via slow manifold approach

Abst rac t -A concept of exact slow optimal control is defined for a general class of nonlinear singularly perturbed systems utilizing the slow manifold theory. Under a set of conditions an exact optimal feedback regulation restricted to the slow manifold is obtained. The result is applied to a class of nonlinear systems with nonlinear fast actuators. It is shown that by adding an extra compensating slow control to the near optimal control an exact optimal feedback regulation is achieved on the manifold. An upper bound on the perturbation parameter is obtained under which the result is valid.