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Published November 2020 | public
Journal Article

An integrative perspective to LQ and ℓ∞ control for delayed and quantized systems

Abstract

Deterministic and stochastic approaches to handle uncertainties may incur very different complexities in computation time and memory usage, in addition to different uncertainty models. For linear systems with delay and rate constrained communications between the observer and the controller, previous work shows that a deterministic approach, the ℓ ∞ control has low complexity but can only handle bounded disturbances. In this article, we take a stochastic approach and propose a linear-quadratic (LQ) controller that can handle arbitrarily large disturbance but has large complexity in time and space. The differences in robustness and complexity of the ℓ ∞ and LQ controllers motivate the design of a hybrid controller that interpolates between the two: The ℓ ∞ controller is applied when the disturbance is not too large (normal mode) and the LQ controller is resorted to otherwise (acute mode). We characterize the switching behavior between the normal and acute modes. Using our theoretical bounds which are supplemented by numerical experiments, we show that the hybrid controller can achieve a sweet spot in the robustness-complexity tradeoff, i.e., reject occasional large disturbance while operating with low complexity most of the time.

Additional Information

© 2020 IEEE. Manuscript received September 29, 2019; revised December 23, 2019; accepted January 11, 2020. Date of publication January 23, 2020; date of current version October 21, 2020. This work was supported by National Science Foundation through NCS program under Grant IIS1735003 and CPS program under Grant CNS1646556, Air Force Office of Scientific Research, and gifts from Cisco, Huawei, and Google. The preliminary result of this article was presented at the IEEE Conference on Decision and Control (CDC), Las Vegas, NV, USA, December 2016 [1]. Recommended by Associate Editor F. Mazenc.

Additional details

Created:
August 20, 2023
Modified:
October 19, 2023