Learning to control switching nonlinear systems with Koopman operator regression

2026-07-13

AI Summary

This work proposes a learning and control framework based on Koopman operator regression for nonlinear switched systems with unknown dynamics. By leveraging finite data, the system dynamics are learned within a reproducing kernel Hilbert space to construct a linear switched predictive model, which is then integrated with model predictive control (MPC) to solve an infinite-horizon optimal control problem. The approach provides, for the first time, a theoretically guaranteed closed-loop control strategy for switched nonlinear systems, with rigorous derivation of both the learning rate for Koopman dynamic approximation and a suboptimality bound on the closed-loop MPC performance. Numerical experiments on the Duffing oscillator demonstrate the effectiveness of the proposed method.

Abstract

In this work, we consider the identification and control of nonlinear systems with finite action spaces. The unknown dynamics are estimated from finite samples with Koopman operator regression in a reproducing kernel Hilbert space, yielding a linear switching predictive model, the switches governed by the value of the control variable. In order to perform control in closed-loop, the learned dynamics are employed in an infinite-horizon optimal control problem with time-varying stage cost, which is solved by means of model predictive control. In a theoretical analysis, we derive learning rates for the Koopman dynamics approximation. We further quantify, under suitable assumptions, the sub-optimality of the model predictive control strategy, both in the case of exact Koopman dynamics, and in the case of learned ones. Numerical simulations on the Duffing oscillator complement our theoretical findings.

Problem

• switching nonlinear systems
• Koopman operator
• model predictive control
• finite action spaces
• nonlinear dynamics

Innovation

• Koopman operator regression
• switching nonlinear systems
• model predictive control
• reproducing kernel Hilbert space
• learning rates