Optimal Competitive-Ratio Control
- Creators
- Sabag, Oron
- Lale, Sahin
- Hassibi, Babak
Abstract
Inspired by competitive policy designs approaches in online learning, new control paradigms such as competitive-ratio and regret-optimal control have been recently proposed as alternatives to the classical H₂ and H_∞ approaches. These competitive metrics compare the control cost of the designed controller against the cost of a clairvoyant controller, which has access to past, present, and future disturbances in terms of ratio and difference, respectively. While prior work provided the optimal solution for the regret-optimal control problem, in competitive-ratio control, the solution is only provided for the sub-optimal problem. In this work, we derive the optimal solution to the competitive-ratio control problem. We show that the optimal competitive ratio formula can be computed as the maximal eigenvalue of a simple matrix, and provide a state-space controller that achieves the optimal competitive ratio. We conduct an extensive numerical study to verify this analytical solution, and demonstrate that the optimal competitive-ratio controller outperforms other controllers on several large scale practical systems. The key techniques that underpin our explicit solution is a reduction of the control problem to a Nehari problem, along with a novel factorization of the clairvoyant controller's cost. We reveal an interesting relation between the explicit solutions that now exist for both competitive control paradigms by formulating a regret-optimal control framework with weight functions that can also be utilized for practical purposes.
Additional Information
Attribution 4.0 International (CC BY 4.0)Attached Files
Submitted - 2206.01782.pdf
Files
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Additional details
- Eprint ID
- 115592
- Resolver ID
- CaltechAUTHORS:20220714-224600473
- Created
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2022-07-15Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field