Koopman-based feedback design with stability guarantees

Abstract

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.

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Cited by in corpus (10)

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• Data-driven MPC with terminal conditions in the Koopman framework
• Data-Driven Predictive Control of Nonholonomic Robots Based on a Bilinear Koopman Realization: Data Does Not Replace Geometry
• Koopman-based control of nonlinear systems with closed-loop guarantees
• End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data
• Koopman-based control using sum-of-squares optimization: Improved stability guarantees and data efficiency
• Robust Control Design and Analysis Based on Lifting Linearization of Nonlinear Systems Under Uncertain Initial Conditions
• Data-Driven Contact-Aware Control Method for Real-Time Deformable Tool Manipulation: A Case Study in the Environmental Swabbing