Towards Data-driven LQR with Koopmanizing Flows⋆. Issue 15 (2022)

• Record Type: Journal Article
• Authors: Bevanda, Petar; Beier, Max; Heshmati-Alamdari, Shahab; Sosnowski, Stefan; Hirche, Sandra
• Is Part Of: IFAC-PapersOnLine. Volume 55:Issue 15(2022)
• Page Start: 13
• Page End: 18
• Publication Date: 2022
• Subjects: Machine learning -- Koopman operators -- Learning for control -- Representation Learning -- Neural networks -- Learning Systems; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2022.07.601
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: We propose a novel framework for learning linear time-invariant (LTI) models for a class of continuous-time non-autonomous nonlinear dynamics based on a representation of Koopman operators. In general, the operator is infinite-dimensional but, crucially, linear. To utilize it for effcient LTI control design, we learn a finite representation of the Koopman operator that is linear in controls while concurrently learning meaningful lifting coordinates. For the latter, we rely on Koopmanizing Flows - a diffeomorphism-based representation of Koopman operators and extend it to systems with linear control entry. With such a learned model, we can replace the nonlinear optimal control problem with quadratic cost to that of a linear quadratic regulator (LQR), facilitating efficacious optimal control for nonlinear systems. The superior control performance of the proposed method is demonstrated on simulation examples.