Data-Driven Optimal Control Using Transfer Operators

In this paper, we propose a data-driven approach for control of nonlinear dynamical systems. The proposed data-driven approach relies on transfer Koopman and Perron-Frobenius ( P-F) operators for linear representation and control of such systems. Systematic model-based frameworks involving linear transfer P-F operator were proposed for almost everywhere stability analysis and control design of a nonlinear dynamical system in previous works [1]-[3]. Lyapunov measure can be used as a tool to provide linear programming-based computational framework for stability analysis and optimal control design of a nonlinear system. In this paper, we show that the Lyapunov measure-based framework can extended to a data-driven setting, where the finite dimensional approximation of linear transfer P-F operator and optimal control can be obtained from time-series data. We exploit the positivity and Markov property of P-F operator to provide linear programming based approach for designing an optimally stabilizing feedback controller.