Optimal Quadratic Regulation of Nonlinear System Using Koopman Operator

Xu Ma, Bowen Huang, Umesh Vaidya

Abstract: In this paper, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite dimensional bilinear system. Optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. Simulation results are presented to demonstrate the application of the developed framework.