Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913339488075776 |
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| author | de Jong, Thomas Breschi, Valentina Schoukens, Maarten Lazar, Mircea |
| author_facet | de Jong, Thomas Breschi, Valentina Schoukens, Maarten Lazar, Mircea |
| contents | 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 model to predict future outputs, we design a subspace predictive controller in the Koopman space. This allows us to learn the observables minimizing the multi-step output prediction error of the Koopman subspace predictor, preventing the propagation of prediction errors. To avoid losing feasibility of our predictive control scheme due to prediction errors, we compute a terminal cost and terminal set in the Koopman space and we obtain recursive feasibility guarantees through an interpolated initial state. As a third contribution, we introduce a novel regularization cost yielding input-to-state stability guarantees with respect to the prediction error for the resulting closed-loop system. The performance of the developed Koopman data-driven predictive control methodology is illustrated on a nonlinear benchmark example from the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_01292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees de Jong, Thomas Breschi, Valentina Schoukens, Maarten Lazar, Mircea Optimization and Control Machine Learning Systems and Control 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 model to predict future outputs, we design a subspace predictive controller in the Koopman space. This allows us to learn the observables minimizing the multi-step output prediction error of the Koopman subspace predictor, preventing the propagation of prediction errors. To avoid losing feasibility of our predictive control scheme due to prediction errors, we compute a terminal cost and terminal set in the Koopman space and we obtain recursive feasibility guarantees through an interpolated initial state. As a third contribution, we introduce a novel regularization cost yielding input-to-state stability guarantees with respect to the prediction error for the resulting closed-loop system. The performance of the developed Koopman data-driven predictive control methodology is illustrated on a nonlinear benchmark example from the literature. |
| title | Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees |
| topic | Optimization and Control Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2405.01292 |