1. Towards Data-driven LQR with Koopmanizing Flows⋆
- Author
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Bevanda, Petar, Beier, Max, Heshmati-Alamdari, Shahab, Sosnowski, Stefan, and Hirche, Sandra
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Mathematics::Dynamical Systems ,Optimization and Control (math.OC) ,Control and Systems Engineering ,FOS: Electrical engineering, electronic engineering, information engineering ,FOS: Mathematics ,Systems and Control (eess.SY) ,Dynamical Systems (math.DS) ,Mathematics - Dynamical Systems ,Electrical Engineering and Systems Science - Systems and Control ,Mathematics - Optimization and Control ,Machine Learning (cs.LG) - 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 efficient 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., Final version, accepted for presentation at the 6th IFAC Conference on Intelligent Control and Automation Sciences (ICONS), 2022. arXiv admin note: text overlap with arXiv:2112.04085
- Published
- 2022