Nonlinear systems which have finite-dimensional H∞ suboptimal central controllers

Following the work of Basar and Bernhard (1990), the authors derived (1993) the nonlinear central controller solving the nonlinear (standard) H_∞ suboptimal control problem. This nonlinear central controller is an infinite-dimensional system, and resembles very much the solution in nonlinear stochastic filtering or nonlinear deterministic filtering. After showing that in the linear case the nonlinear central controller reduces to the finite-dimensional central controller, we consider in the present note the question if there are truly nonlinear systems having finite-dimensional central controllers. Guided by similar considerations in nonlinear stochastic and deterministic filtering, we characterize a specific class of nonlinear systems having finite-dimensional central controllers. This class can be regarded as the deterministic H_∞ analogue of the class of nonlinear systems admitting finite dimensional filters as identified by Benes (1981).