Energy-Gain Control of Time-Varying Systems: Receding Horizon Approximation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913150581866496 |
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| author | Sun, Jintao Cantoni, Michael |
| author_facet | Sun, Jintao Cantoni, Michael |
| contents | Standard formulations of prescribed worst-case disturbance energy-gain control policies for linear time-varying systems depend on all forward model data. In discrete time, this dependence arises through a backward Riccati recursion. This article is about the infinite-horizon $\ell_2$ gain performance of state feedback policies with only finite receding-horizon preview of the model parameters. The proposed synthesis of controllers subject to such a constraint leverages the strict contraction of lifted Riccati operators under uniform controllability and observability. The main approximation result is a sufficient number of preview steps for the incurred performance loss to remain below any set tolerance, relative to the baseline gain bound of the associated infinite-preview controller. Aspects of the result are explored in a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy-Gain Control of Time-Varying Systems: Receding Horizon Approximation Sun, Jintao Cantoni, Michael Optimization and Control Systems and Control Standard formulations of prescribed worst-case disturbance energy-gain control policies for linear time-varying systems depend on all forward model data. In discrete time, this dependence arises through a backward Riccati recursion. This article is about the infinite-horizon $\ell_2$ gain performance of state feedback policies with only finite receding-horizon preview of the model parameters. The proposed synthesis of controllers subject to such a constraint leverages the strict contraction of lifted Riccati operators under uniform controllability and observability. The main approximation result is a sufficient number of preview steps for the incurred performance loss to remain below any set tolerance, relative to the baseline gain bound of the associated infinite-preview controller. Aspects of the result are explored in a numerical example. |
| title | Energy-Gain Control of Time-Varying Systems: Receding Horizon Approximation |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2512.21051 |