Sufficient conditions for feasibility of optimal control problems using Control Barrier Functions
It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions...
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| Published in | Automatica (Oxford) Vol. 135; p. 109960 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.01.2022
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| Abstract | It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in this approach is ensuring the feasibility of these QPs, especially under tight control bounds and safety constraints of high relative degree. The main contribution of this paper is to provide sufficient conditions for guaranteed feasibility. The sufficient conditions are captured by a single constraint that is enforced by a CBF, which is added to the QPs such that their feasibility is always guaranteed. The additional constraint is designed to be always compatible with the existing constraints, therefore, it cannot make a feasible set of constraints infeasible — it can only increase the overall feasibility. We illustrate the effectiveness of the proposed approach on an adaptive cruise control problem. |
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| AbstractList | It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in this approach is ensuring the feasibility of these QPs, especially under tight control bounds and safety constraints of high relative degree. The main contribution of this paper is to provide sufficient conditions for guaranteed feasibility. The sufficient conditions are captured by a single constraint that is enforced by a CBF, which is added to the QPs such that their feasibility is always guaranteed. The additional constraint is designed to be always compatible with the existing constraints, therefore, it cannot make a feasible set of constraints infeasible — it can only increase the overall feasibility. We illustrate the effectiveness of the proposed approach on an adaptive cruise control problem. |
| ArticleNumber | 109960 |
| Author | Cassandras, Christos G. Belta, Calin A. Xiao, Wei |
| Author_xml | – sequence: 1 givenname: Wei surname: Xiao fullname: Xiao, Wei email: xiaowei@bu.edu – sequence: 2 givenname: Calin A. surname: Belta fullname: Belta, Calin A. email: cbelta@bu.edu – sequence: 3 givenname: Christos G. surname: Cassandras fullname: Cassandras, Christos G. email: cgc@bu.edu |
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| Cites_doi | 10.1109/LCSYS.2017.2710943 10.1109/TAC.2007.902736 10.1109/CDC42340.2020.9303857 10.1016/j.automatica.2008.11.017 10.1109/CDC.2013.6760627 10.23919/ACC.2019.8814657 10.1109/CDC.2013.6760091 10.1109/CDC.2014.7040372 10.1109/ACCESS.2015.2419630 10.3182/20070822-3-ZA-2920.00076 10.1109/ACC.2015.7171033 10.1109/CDC40024.2019.9029455 10.1109/ACC.2015.7172044 10.1109/LCSYS.2018.2853182 10.1145/3450267.3450542 10.1109/ACC.2016.7524935 10.1109/CDC.2012.6426229 |
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| Keywords | Control Barrier Function Safety-critical control Optimal control Lyapunov methods |
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| References_xml | – reference: Xiao, W., Mehdipour, N., Collin, A., Bin-Nun, A., Frazzoli, E., Tebbens, R., & Belta, C. (2021). Rule-based optimal control for autonomous driving. In – reference: Hsu, S. C., Xu, X., & Ames, A. D. (2015). Control barrier function based quadratic programs with application to bipedal robotic walking. In – volume: 3 start-page: 96 year: 2019 end-page: 101 ident: b12 article-title: Control barrier functions for signal temporal logic tasks publication-title: IEEE Control Systems Letters – year: 2002 ident: b11 article-title: Nonlinear systems – reference: (pp. 4542–4548). – reference: (pp. 6271–6278). – reference: Panagou, D., Stipanovic, D. M., & Voulgaris, P. G. (2013). Multi-objective control for multi-agent systems using Lyapunov-like barrier functions. 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In – volume: 1 start-page: 310 issue: 2 year: 2017 ident: 10.1016/j.automatica.2021.109960_b9 article-title: Nonsmooth barrier functions with applications to multi-robot systems publication-title: IEEE Control Systems Letters doi: 10.1109/LCSYS.2017.2710943 – volume: 52 start-page: 1415 issue: 8 year: 2007 ident: 10.1016/j.automatica.2021.109960_b15 article-title: A framework for worst-case and stochastic safety verification using barrier certificates publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2007.902736 – year: 2018 ident: 10.1016/j.automatica.2021.109960_b16 – ident: 10.1016/j.automatica.2021.109960_b22 doi: 10.1109/CDC42340.2020.9303857 – volume: 45 start-page: 918 issue: 4 year: 2009 ident: 10.1016/j.automatica.2021.109960_b17 article-title: Barrier lyapunov functions for the control of output-constrained nonlinear systems publication-title: Automatica doi: 10.1016/j.automatica.2008.11.017 – ident: 10.1016/j.automatica.2021.109960_b19 doi: 10.1109/CDC.2013.6760627 – ident: 10.1016/j.automatica.2021.109960_b25 doi: 10.23919/ACC.2019.8814657 – year: 2002 ident: 10.1016/j.automatica.2021.109960_b11 – year: 2009 ident: 10.1016/j.automatica.2021.109960_b4 – year: 2004 ident: 10.1016/j.automatica.2021.109960_b5 – ident: 10.1016/j.automatica.2021.109960_b14 doi: 10.1109/CDC.2013.6760091 – ident: 10.1016/j.automatica.2021.109960_b3 doi: 10.1109/CDC.2014.7040372 – volume: 3 start-page: 323 year: 2015 ident: 10.1016/j.automatica.2021.109960_b8 article-title: Torque saturation in bipedal robotic walking through control lyapunov function based quadratic programs publication-title: IEEE Access doi: 10.1109/ACCESS.2015.2419630 – year: 2003 ident: 10.1016/j.automatica.2021.109960_b7 – year: 1969 ident: 10.1016/j.automatica.2021.109960_b6 – ident: 10.1016/j.automatica.2021.109960_b18 doi: 10.3182/20070822-3-ZA-2920.00076 – ident: 10.1016/j.automatica.2021.109960_b20 doi: 10.1109/ACC.2015.7171033 – ident: 10.1016/j.automatica.2021.109960_b21 doi: 10.1109/CDC40024.2019.9029455 – ident: 10.1016/j.automatica.2021.109960_b10 doi: 10.1109/ACC.2015.7172044 – volume: 3 start-page: 96 issue: 1 year: 2019 ident: 10.1016/j.automatica.2021.109960_b12 article-title: Control barrier functions for signal temporal logic tasks publication-title: IEEE Control Systems Letters doi: 10.1109/LCSYS.2018.2853182 – ident: 10.1016/j.automatica.2021.109960_b24 doi: 10.1145/3450267.3450542 – ident: 10.1016/j.automatica.2021.109960_b13 doi: 10.1109/ACC.2016.7524935 – year: 2006 ident: 10.1016/j.automatica.2021.109960_b1 – ident: 10.1016/j.automatica.2021.109960_b2 doi: 10.1109/CDC.2012.6426229 – year: 2021 ident: 10.1016/j.automatica.2021.109960_b23 article-title: Adaptive control barrier functions publication-title: IEEE Transactions on Automatic Control |
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| SubjectTerms | Control Barrier Function Lyapunov methods Optimal control Safety-critical control |
| Title | Sufficient conditions for feasibility of optimal control problems using Control Barrier Functions |
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