A Framework for Time-Varying Optimization via Derivative Estimation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909154081243136 |
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| author | Marchi, Matteo Bunton, Jonathan Silvestre, João Pedro Tabuada, Paulo |
| author_facet | Marchi, Matteo Bunton, Jonathan Silvestre, João Pedro Tabuada, Paulo |
| contents | Optimization algorithms have a rich and fundamental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time -- typically in response to a dynamically changing environment -- online optimization becomes a continuous-time trajectory tracking problem. To accommodate these time variations, one typically requires some inherent knowledge about their nature such as a time derivative.
In this paper, we propose a novel construction and analysis of a continuous-time derivative estimation scheme based on "dirty-derivatives", and show how it naturally interfaces with continuous-time optimization algorithms using the language of ISS (Input-to-State Stability). More generally, we show how a simple Lyapunov redesign technique leads to provable suboptimality guarantees when composing this estimator with any well-behaved optimization algorithm for time-varying costs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Framework for Time-Varying Optimization via Derivative Estimation Marchi, Matteo Bunton, Jonathan Silvestre, João Pedro Tabuada, Paulo Optimization and Control Systems and Control Optimization algorithms have a rich and fundamental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time -- typically in response to a dynamically changing environment -- online optimization becomes a continuous-time trajectory tracking problem. To accommodate these time variations, one typically requires some inherent knowledge about their nature such as a time derivative. In this paper, we propose a novel construction and analysis of a continuous-time derivative estimation scheme based on "dirty-derivatives", and show how it naturally interfaces with continuous-time optimization algorithms using the language of ISS (Input-to-State Stability). More generally, we show how a simple Lyapunov redesign technique leads to provable suboptimality guarantees when composing this estimator with any well-behaved optimization algorithm for time-varying costs. |
| title | A Framework for Time-Varying Optimization via Derivative Estimation |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2403.19088 |