Koopman-based feedback design with stability guarantees
We present a method to design a state-feedback controller ensuring exponential stability for nonlinear systems using only measurement data. Our approach relies on Koopman-operator theory and uses robust control to explicitly account for approximation errors due to finitely many data samples. To simplify practical usage across various applications, we provide a tutorial-style exposition of the feedback design and its stability guarantees for single-input systems. Moreover, we extend this controller design to multi-input systems and more flexible nonlinear state-feedback controllers using gain-scheduling techniques to increase the guaranteed region of attraction. As the proposed controller design is framed as a semidefinite program, it allows for an efficient solution. Further, we enhance the geometry of the region of attraction through a heuristic algorithm that establishes a connection between the employed Koopman lifting and the dynamics of the system. Finally, we validate the proposed feedback design procedure by means of numerical examples.
Code (0)
등록된 구현이 없습니다.
Tasks
SchedulingSimilar Papers 제목 키워드 기반
Learning Stable Koopman Embeddings for Identification and Control
This paper introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take …
Imitation LearningKoopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees
In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman …
PredictionNeural Koopman Lyapunov Control
Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems…
Data-Driven Control of Linear Parabolic Systems using Koopman Eigenstructure Assignment
This paper considers the data-driven stabilization of linear boundary controlled parabolic PDEs by making use of the Koopman operator. For this, a Koopman eigenstructure assignment problem is solved, which amounts to det…
Koopman-based control of nonlinear systems with closed-loop guarantees
In this paper, we provide a tutorial overview and an extension of a recently developed framework for data-driven control of unknown nonlinear systems with rigorous closed-loop guarantees. The proposed approach relies on …