Online convex optimization for constrained control of linear systems using a reference governor
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916498790940672 |
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| author | Nonhoff, Marko Köhler, Johannes Müller, Matthias A. |
| author_facet | Nonhoff, Marko Köhler, Johannes Müller, Matthias A. |
| contents | In this work, we propose a control scheme for linear systems subject to pointwise in time state and input constraints that aims to minimize time-varying and a priori unknown cost functions. The proposed controller is based on online convex optimization and a reference governor. In particular, we apply online gradient descent to track the time-varying and a priori unknown optimal steady state of the system. Moreover, we use a $λ$-contractive set to enforce constraint satisfaction and a sufficient convergence rate of the closed-loop system to the optimal steady state. We prove that the proposed scheme is recursively feasible, ensures that the state and input constraints are satisfied at all times, and achieves a dynamic regret that is linearly bounded by the variation of the cost functions. The algorithm's performance and constraint satisfaction is illustrated by means of a simulation example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_09088 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Online convex optimization for constrained control of linear systems using a reference governor Nonhoff, Marko Köhler, Johannes Müller, Matthias A. Systems and Control Optimization and Control In this work, we propose a control scheme for linear systems subject to pointwise in time state and input constraints that aims to minimize time-varying and a priori unknown cost functions. The proposed controller is based on online convex optimization and a reference governor. In particular, we apply online gradient descent to track the time-varying and a priori unknown optimal steady state of the system. Moreover, we use a $λ$-contractive set to enforce constraint satisfaction and a sufficient convergence rate of the closed-loop system to the optimal steady state. We prove that the proposed scheme is recursively feasible, ensures that the state and input constraints are satisfied at all times, and achieves a dynamic regret that is linearly bounded by the variation of the cost functions. The algorithm's performance and constraint satisfaction is illustrated by means of a simulation example. |
| title | Online convex optimization for constrained control of linear systems using a reference governor |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2211.09088 |