Quadratic regulatory theory for analytic non-linear systems with additive controls

Abstract

Quadratic regulator problems over finite and infinite time intervals are solved for non-linear systems which are analytic in the state and linear in the control. The solution approach is based on using a formal power series expansion method for solving a non-linear Hamiltonian system. The technique of Carleman linearization facilitates the approach. The unique solution to the non-linear optimal regulator problem is obtained in terms of a convergent power series which satisfies the Hamilton-Jacobi-Bellman equation of dynamic programming. The realization of the optimal regulator is investigated and sufficient conditions are derived from the optimal regulator using the technique of Carleman linearization. Several examples are given to illustrate the theory. © 1989.