Proves recursive feasibility and asymptotic stability for data-driven Koopman MPC with terminal conditions under a proportional error bound, applicable via kEDMD to broad nonlinear systems and shown in a numerical example.
On excitation of control-affine systems and its use for data-driven Koopman approximants
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abstract
The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems. However, extensions towards control-affine systems resulting in bilinear surrogate models are prone to demanding data requirements rendering their applicability intricate. In this paper, we propose a framework for data-fitting of control-affine mappings to increase the robustness margin in the associated system identification problem and, thus, to provide reliable bilinear EDMD schemes. In particular, guidelines for input selection based on subspace angles are deduced such that a desired threshold with respect to the minimal singular value is ensured. Moreover, we derive necessary and sufficient conditions of optimality for maximizing the minimal singular value. Further, we demonstrate the usefulness of the proposed approach using bilinear EDMD with control for nonholonomic robots.
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UNVERDICTED 2representative citing papers
A hierarchical RL-OC method uses inverse optimization to derive structured lower-level policies from demonstrations, claiming superior efficiency and quality over end-to-end RL and existing hierarchical baselines on two control tasks.
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Hierarchical Decision Making with Structured Policies: A Principled Design via Inverse Optimization
A hierarchical RL-OC method uses inverse optimization to derive structured lower-level policies from demonstrations, claiming superior efficiency and quality over end-to-end RL and existing hierarchical baselines on two control tasks.