A Fixed-Architecture Framework for Stochastic Nonlinear Controller Synthesis

Ethan N. Evans, Wassim M. Haddad, Evangelos A. Theodorou

Abstract: In this paper, we present a Lyapunov function-based optimization approach for designing state and output feedback control laws for systems with polynomial nonlinearities. We use local polynomial expansions of a chosen order to approximate a higher-order nonlinear stochastic dynamical system, reformulate stochastic asymptotic stability conditions in the form of a nonlinear constrained optimization problem, and computationally determine the domain of attraction of the synthesized nonlinear controller on the original system. Finally, we illustrate the effectiveness of the proposed algorithm on two illustrative numerical examples.