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Mathematics > Optimization and Control

arXiv:2210.01978 (math)
[Submitted on 5 Oct 2022 (v1), last revised 9 Dec 2022 (this version, v3)]

Title:Control Synthesis for Stability and Safety by Differential Complementarity Problem

Authors:Yinzhuang Yi, Shumon Koga, Bogdan Gavrea, Nikolay Atanasov
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Abstract:This paper develops a novel control synthesis method for safe stabilization of control-affine systems as a Differential Complementarity Problem (DCP). Our design uses a control Lyapunov function (CLF) and a control barrier function (CBF) to define complementarity constraints in the DCP formulation to certify stability and safety, respectively. The CLF-CBF-DCP controller imposes stability as a soft constraint, which is automatically relaxed when the safety constraint is active, without the need for parameter tuning or optimization. We study the closed-loop system behavior with the CLF-CBF-DCP controller and identify conditions on the existence of local equilibria. Although in certain cases the controller yields undesirable local equilibria, those can be confined to a small subset of the safe set boundary by proper choice of the control parameters. Then, our method can avoid undesirable equilibria that CLF-CBF quadratic programming techniques encounter.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2210.01978 [math.OC]
  (or arXiv:2210.01978v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.01978
Related DOI: https://doi.org/10.1109/LCSYS.2022.3228726

Submission history

From: Yinzhuang Yi [view email]
[v1] Wed, 5 Oct 2022 01:10:06 UTC (701 KB)
[v2] Wed, 30 Nov 2022 21:28:10 UTC (685 KB)
[v3] Fri, 9 Dec 2022 19:24:40 UTC (1,612 KB)
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