Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems

Abstract

The problem considered is to optimally control the nonlinear system: x = a1(x) + A1(x)z + B1(x)u, x(0) = xo (1a) µz = a2(x) + A2(x)z + B2(x)u, z(0) = zo (1b) with respect to the performance index J=¿0 ¿[p(x) + s'(x)z + z'Q(x)z + u'R(x)u]dt (2) where µ > 0 is the small singular perturbation parameter, x, z are n-, m- dimensional states, respectively, and u is an r-dimensional control.