Robust regret optimal control

Author:

Liu Jietian1,Seiler Peter1

Affiliation:

1. Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor Michigan USA

Abstract

SummaryThis paper presents a synthesis method for robust, regret optimal control. The plant is modeled in discrete‐time by an uncertain linear time‐invariant (LTI) system. An optimal non‐causal controller is constructed using the nominal plant model and given full knowledge of the disturbance. Robust regret is defined relative to the performance of this optimal non‐causal control. It is shown that a controller achieves robust regret if and only if it satisfies a robust performance condition. DK‐iteration can be used to synthesize a controller that satisfies this condition and hence achieve a given level of robust regret. The approach is demonstrated two examples: (i) a single‐input, single‐output (SISO) classical design, and (ii) an active suspension for a quarter car model. The SISO example is simple but is intended to provide insight about the robust regret control design. The quarter car example compares the robust regret controllers against regret controllers designed without plant uncertainty.

Publisher

Wiley

Reference39 articles.

1. GoelG HassibiB.Regret‐optimal control in dynamic environments. arXiv preprint arXiv:2010.104732020.

2. GoelG WiermanA.“An online algorithm for smoothed regression and LQR control ” Paper presented at: The 22nd International Conference on Artificial Intelligence and Statistics. PMLR.20192504–2513.

3. GoelG HassibiB.“The power of linear controllers in LQR control ” Paper presented at: IEEE Conference on Decision and Control. IEEE.20226652–6657.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Regret-Optimal Control under Partial Observability;2024 American Control Conference (ACC);2024-07-10

2. Robust regret optimal control;International Journal of Robust and Nonlinear Control;2024-01-11

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