Finite-time composite control for a class of singularly perturbed nonlinear systems via successive Galerkin approximation

This paper presents a ne algorithm of the finite-time closed-loop composite control for a class of singularly perturbed nonlinear systems ith respect to performance criteria, using the successive Galerki approximatio (SGA). The singularly perturbed nonlinear system is decomposed into t o subsystems of a slo -time scale and a fast-time scale via singular perturbatio theory, and the t o optimal control la s are obtained to each subsystem using the SGA method. Composite control theory guarantees near-optimal closed-loop performance but the resulting problem is difficult to solve for nonlinear systems. To overcome the difficulties inherent i the optimal control problem, the suitable optimal feedback control la ca be constructed i term of the approximated solutio to a Hamilton-Jacobi-Bellma equatio using SGA. The finite-time composite control la for singularly perturbed nonlinear systems is designed by a linear combinatio of the slo and fast variables.