Joint Stabilization and Regret Minimization through Switching in Over-Actuated Systems (extended version)

Chekan, Jafar Abbaszadeh; Azizzadenesheli, Kamyar; Langbort, Cédric

doi:10.48550/arxiv.2105.14709

Cited by 2 publications

(4 citation statements)

References 15 publications

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“…As such, the algorithms update the estimate and policy when the condition det(V j t ) > 2 det(V j τ ) is fulfilled where τ is the last time the policy got updated (τ is solely used in Algorithm 2 and should not be mixed with switch times in actuating modes; τ i s). This is a standard step in OFU-based algorithms ( [29], [32], and [33]).…”

Section: Control Designmentioning

confidence: 99%

“…and V i [0 t] and Θi t is given by (32,33). On the other when the projection is not applied the confidence set is given as follows:…”

Section: Stability Analysismentioning

confidence: 99%

“…T ) regret bound with statespace dimension of p. Authors in [31] proposed an OFU-based learning algorithm with mild assumptions and O( √ T ) regret. Furthermore, in [32] propose an OFU-based algorithm which for joint stabilization and regret minimization that leverages actuator redundancy to alleviate state explosion during initial time steps when there is low number of data.…”

mentioning

confidence: 99%

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Learn and Control while Switching: with Guaranteed Stability and Sublinear Regret

Chekan¹,

Langbort²

2022

Preprint

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Over-actuated systems often make it possible to achieve specific performances by switching between different subsets of actuators. However, when the system parameters are unknown, transferring authority to different subsets of actuators is challenging due to stability and performance efficiency concerns. This paper presents an efficient algorithm to tackle the so-called "learn and control while switching between different actuating modes" problem in the Linear Quadratic (LQ) setting. Our proposed strategy is constructed upon Optimism in the Face of Uncertainty (OFU) based algorithm equipped with a projection toolbox to keep the algorithm efficient, regret-wise. Along the way, we derive an optimum duration for the warm-up phase, thanks to the existence of a stabilizing neighborhood. The stability of the switched system is also guaranteed by designing a minimum average dwell time. The proposed strategy is proved to have a regret bound of Ō √ T + O ns √ T in horizon T with (ns) number of switches, provably outperforming naively applying the basic OFU algorithm.

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Section: Control Designmentioning

confidence: 99%

“…and V i [0 t] and Θi t is given by (32,33). On the other when the projection is not applied the confidence set is given as follows:…”

Section: Stability Analysismentioning

confidence: 99%

mentioning

confidence: 99%

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Learn and Control while Switching: with Guaranteed Stability and Sublinear Regret

Chekan¹,

Langbort²

2022

Preprint

Self Cite

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“…In this fashion, (Ibrahimi et al, 2012) introduced O(p √ T ) regret algorithm with state-space dimension of p. (Lale et al, 2022) applied the OFU principle and, through imposing extra exploratory noise, accelerated the stabilization of the system. (Chekan et al, 2021) introduced an OFU-based strategy for joint stabilization and regret minimization of over-actuated systems. (Cohen et al, 2019) formulated the OFU-based approach in a relaxed semi-definite program (SDP) and, as such, proposed a computationally efficient counterpart of the algorithm from (Abbasi-Yadkori & Szepesvári, 2011), which involves solving a non-convex optimization program.…”

Section: Introductionmentioning

confidence: 99%

Fast and Safe Switching with Guaranteed Regret: LQR Setting with Unknown Dynamics

Chekan¹,

Langbort²

2023

Preprint

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Stability guarantees of the Externally forced switched (EFS) system in which switches occur deliberately to fulfill an exogenous reason is a crucial problem. High frequent switches, however, can cause instability in switched systems even when all closed-loop modes are stable. The control community has already addressed this classic problem with a known system model by designing a minimum dwell time. However, the gap still exists in the lack of such knowledge and especially when fast switching is deemed necessary. In this work, we aim to address the challenge in LQR setting and within the framework of our posed problem, in which, after a switch, the next mode reveals to switch to, and the task is to make the subsequent switching quickly while guaranteeing boundedness of state norm. We address the problem by designing an OFU-based algorithm that couples system identification and control design procedures. Parallel to the control design, our proposed algorithm also guarantees safe switches based on its estimated dwell time. With a provably tight dwell-time estimate error, we show that our proposed strategy achieves the expected regret of O(|M| √ ns), where ns and |M| are the total number of switches and the number of modes respectively, compared to the case when all parameters are known. To the best of the authors' knowledge, this is the first work for learning dwell time with guaranteed performance.

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Joint Stabilization and Regret Minimization through Switching in Over-Actuated Systems (extended version)

Cited by 2 publications

References 15 publications

Learn and Control while Switching: with Guaranteed Stability and Sublinear Regret

Learn and Control while Switching: with Guaranteed Stability and Sublinear Regret

Fast and Safe Switching with Guaranteed Regret: LQR Setting with Unknown Dynamics

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