2020/10/05 by Bowen Huang, Huang, Bowen, Umesh Vaidya +1 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2010.01742
openalex publication_date 2020/10/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The paper is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system dynamics is available in the form of time-series data. We provide a convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the dynamical system's stability theory involving density function and Perron-Frobenius operator. We formulate the optimal control problem as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the Koopman operator's data-driven computation, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.