A Convex Data-Driven Approach for Nonlinear Control Synthesis

Hyungjin Choi, Umesh Vaidya and Yongxin Chen
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Hyungjin Choi: Energy Storage Technology and Systems at Sandia National Laboratories, Albuquerque, NM 87185, USA
Umesh Vaidya: Department of Mechanical Enginerring, Clemson University, Clemson, SC 29634, USA
Yongxin Chen: School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

Mathematics, 2021, vol. 9, issue 19, 1-12

Abstract: We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

Keywords: nonlinear control; Koopman operator; sum of squares (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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