Towards Data-driven LQR with Koopmanizing Flows
This addresses the challenge of efficient optimal control for nonlinear systems, which is incremental as it extends existing Koopman operator methods to include linear control entry.
The paper tackles the problem of controlling nonlinear systems by learning linear time-invariant models using Koopman operators, enabling the use of linear quadratic regulator (LQR) methods for optimal control, with results demonstrating superior performance in simulations.
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.