Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

Williams, Alan Brian; Krstic, Miroslav; Scheinker, Alexander

doi:10.1109/tac.2024.3469785

Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

Journal Article · Fri Sep 27 00:00:00 EDT 2024 · IEEE Transactions on Automatic Control

DOI:https://doi.org/10.1109/tac.2024.3469785· OSTI ID:2478087

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University of California, San Diego, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
University of California, San Diego, CA (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

We introduce a safe extremum-seeking (Safe ES) algorithm which achieves the minimization of an unknown objective function while ensuring that an unknown, yet measured, control barrier function (CBF) remains above an arbitrarily small negative value for all time. In other words, “practical safety” is maintained during the entire period of convergence to the constrained extremum. Our design is based on quadratic program (QP) CBF style filters for safety, which is applied in an average and estimated sense. Using nonsmooth analysis tools, we guarantee semiglobal practical asymptotic (SPA) stability of the global constrained optimum, practical convergence to the safe set if starting in a condition violating the CBF, and practical safety for all time—semiglobally—if starting in safe set. The safety result of the paper is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients which guarantee that such a small violation is not exceeded. The paper outlines a set of sufficient conditions on the barrier and objective functions, and by way of a Lyapunov argument, we demonstrate that nonconvex constrained optimization problems can be solved. We present these results in the setting of a static map and a dynamical system. A simulation example illustrates the results.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2478087

Report Number(s):: LA-UR--24-23906

Journal Information:: IEEE Transactions on Automatic Control, Journal Name: IEEE Transactions on Automatic Control Journal Issue: 3 Vol. 70; ISSN 0018-9286

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

References (50)

Stability of extremum seeking feedback for general nonlinear dynamic systems Krstić, Miroslav; Wang, Hsin-Hsiung Automatica, Vol. 36, Issue 4 https://doi.org/10.1016/S0005-1098(99)00183-1	journal	April 2000
Parameter convergence in adaptive extremum-seeking control Adetola, V.; Guay, M. Automatica, Vol. 43, Issue 1 https://doi.org/10.1016/j.automatica.2006.07.021	journal	January 2007
On global extremum seeking in the presence of local extrema Tan, Y.; Nešić, D.; Mareels, I. M. Y. Automatica, Vol. 45, Issue 1 https://doi.org/10.1016/j.automatica.2008.06.010	journal	January 2009
Multivariable Newton-based extremum seeking Ghaffari, Azad; Krstić, Miroslav; Nešić, Dragan Automatica, Vol. 48, Issue 8 https://doi.org/10.1016/j.automatica.2012.05.059	journal	August 2012
Unified frameworks for sampled-data extremum seeking control: Global optimisation and multi-unit systems Khong, Sei Zhen; Nešić, Dragan; Tan, Ying Automatica, Vol. 49, Issue 9 https://doi.org/10.1016/j.automatica.2013.06.020	journal	September 2013
A time-varying extremum-seeking control approach Guay, Martin; Dochain, Denis Automatica, Vol. 51 https://doi.org/10.1016/j.automatica.2014.10.078	journal	January 2015
Shahshahani gradient-like extremum seeking Poveda, Jorge I.; Quijano, Nicanor Automatica, Vol. 58 https://doi.org/10.1016/j.automatica.2015.05.002	journal	August 2015
A framework for a class of hybrid extremum seeking controllers with dynamic inclusions Poveda, Jorge I.; Teel, Andrew R. Automatica, Vol. 76 https://doi.org/10.1016/j.automatica.2016.10.029	journal	February 2017
Constrained extremum seeking of a MIMO dynamic system Liao, Chwen-Kai; Manzie, Chris; Chapman, Airlie Automatica, Vol. 108 https://doi.org/10.1016/j.automatica.2019.108496	journal	October 2019
Bridging the gap between optimal trajectory planning and safety-critical control with applications to autonomous vehicles Xiao, Wei; Cassandras, Christos G.; Belta, Calin A. Automatica, Vol. 129 https://doi.org/10.1016/j.automatica.2021.109592	journal	July 2021
Sampled-data extremum-seeking framework for constrained optimization of nonlinear dynamical systems Hazeleger, Leroy; Nešić, Dragan; van de Wouw, Nathan Automatica, Vol. 142 https://doi.org/10.1016/j.automatica.2022.110415	journal	August 2022
100 years of extremum seeking: A survey Scheinker, Alexander Automatica, Vol. 161 https://doi.org/10.1016/j.automatica.2023.111481	journal	March 2024
Constrained Extremum Seeking: a Modified-Barrier Function Approach Labar, Christophe; Garone, Emanuele; Kinnaert, Michel IFAC-PapersOnLine, Vol. 52, Issue 16 https://doi.org/10.1016/j.ifacol.2019.12.043	journal	January 2019
Extremum seeking with bounded update rates Scheinker, Alexander; Krstić, Miroslav Systems & Control Letters, Vol. 63 https://doi.org/10.1016/j.sysconle.2013.10.004	journal	January 2014
Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions Bacciotti, Andrea; Ceragioli, Francesca ESAIM: Control, Optimisation and Calculus of Variations, Vol. 4 https://doi.org/10.1051/cocv:1999113	journal	January 1999
Adaptive autoencoder latent space tuning for more robust machine learning beyond the training set for six-dimensional phase space diagnostics of a time-varying ultrafast electron-diffraction compact accelerator Scheinker, Alexander; Cropp, Frederick; Filippetto, Daniele Physical Review E, Vol. 107, Issue 4 https://doi.org/10.1103/PhysRevE.107.045302	journal	April 2023
Demonstration of Model-Independent Control of the Longitudinal Phase Space of Electron Beams in the Linac-Coherent Light Source with Femtosecond Resolution Scheinker, Alexander; Edelen, Auralee; Bohler, Dorian Physical Review Letters, Vol. 121, Issue 4 https://doi.org/10.1103/PhysRevLett.121.044801	journal	July 2018
Solving smooth and nonsmooth multivariable extremum seeking problems by the methods of nonlinear programming Teel, A. R.; Popovic, D. Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148) https://doi.org/10.1109/ACC.2001.946111	conference	January 2001
Safety-critical and constrained geometric control synthesis using control Lyapunov and control Barrier functions for systems evolving on manifolds Wu, Guofan; Sreenath, Koushil 2015 American Control Conference (ACC) https://doi.org/10.1109/ACC.2015.7171033	conference	July 2015
Control barrier function based quadratic programs with application to bipedal robotic walking Hsu, Shao-Chen; Xu, Xiangru; Ames, Aaron D. 2015 American Control Conference (ACC) https://doi.org/10.1109/ACC.2015.7172044	conference	July 2015
A unifying approach to extremum seeking: Adaptive schemes based on estimation of derivatives Nesic, D.; Tan, Y.; Moase, W. H. 49th IEEE Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC.2010.5717929	conference	December 2010
A smooth vector field for saddle point problems Durr, Hans-Bernd; Ebenbauer, Christian IEEE Conference on Decision and Control and European Control Conference https://doi.org/10.1109/CDC.2011.6161102	conference	December 2011
A geometric phasor extremum seeking control approach with measured constraints Atta, Khalid Tourkey; Guay, Martin; Lucchese, Riccardo 2019 IEEE 58th Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC40024.2019.9030060	conference	December 2019
Approximate Optimal Control for Safety-Critical Systems with Control Barrier Functions Cohen, Max H.; Belta, Calin 2020 59th IEEE Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC42340.2020.9303896	conference	December 2020
Semi-Global Practical Extremum Seeking with Practical Safety Williams, Alan; Krstic, Miroslav; Scheinker, Alexander 2023 62nd IEEE Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC49753.2023.10383630	conference	December 2023
Practically Safe Extremum Seeking Williams, Alan; Krstic, Miroslav; Scheinker, Alexander 2022 IEEE 61st Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC51059.2022.9993069	conference	December 2022
Input-to-State Safety With Control Barrier Functions Kolathaya, Shishir; Ames, Aaron D. IEEE Control Systems Letters, Vol. 3, Issue 1 https://doi.org/10.1109/LCSYS.2018.2853698	journal	January 2019
Guaranteed Safe Spacecraft Docking With Control Barrier Functions Breeden, Joseph; Panagou, Dimitra IEEE Control Systems Letters, Vol. 6 https://doi.org/10.1109/LCSYS.2021.3136813	journal	January 2022
Safe and Robust Observer-Controller Synthesis Using Control Barrier Functions Agrawal, Devansh R.; Panagou, Dimitra IEEE Control Systems Letters, Vol. 7 https://doi.org/10.1109/LCSYS.2022.3185142	journal	January 2023
A unified framework for input-to-state stability in systems with two time scales Teel, A. R.; Moreau, L.; Nesic, D. IEEE Transactions on Automatic Control, Vol. 48, Issue 9 https://doi.org/10.1109/TAC.2003.816966	journal	September 2003
Nonovershooting Control of Strict-Feedback Nonlinear Systems Krstic, Miroslav; Bement, Matt IEEE Transactions on Automatic Control, Vol. 51, Issue 12 https://doi.org/10.1109/TAC.2006.886518	journal	December 2006
A Framework for Extremum Seeking Control of Systems With Parameter Uncertainties Nesic, Dragan; Mohammadi, Alireza; Manzie, Chris IEEE Transactions on Automatic Control, Vol. 58, Issue 2 https://doi.org/10.1109/TAC.2012.2215270	journal	February 2013
Minimum-Seeking for CLFs: Universal Semiglobally Stabilizing Feedback Under Unknown Control Directions Scheinker, Alexander; Krstic, Miroslav IEEE Transactions on Automatic Control, Vol. 58, Issue 5 https://doi.org/10.1109/TAC.2012.2225514	journal	May 2013
Extremum Seeking for Constrained Inputs Tan, Ying; Li, Yuping; Mareels, Iven M. Y. IEEE Transactions on Automatic Control, Vol. 58, Issue 9 https://doi.org/10.1109/TAC.2013.2254638	journal	September 2013
Stochastic Averaging in Discrete Time and its Applications to Extremum Seeking Liu, Shu-Jun; Krstic, Miroslav IEEE Transactions on Automatic Control, Vol. 61, Issue 1 https://doi.org/10.1109/TAC.2015.2427672	journal	January 2016
Extremum Seeking for Static Maps With Delays Oliveira, Tiago Roux; Krstic, Miroslav; Tsubakino, Daisuke IEEE Transactions on Automatic Control, Vol. 62, Issue 4 https://doi.org/10.1109/TAC.2016.2564958	journal	April 2017
Control Barrier Function Based Quadratic Programs for Safety Critical Systems Ames, Aaron D.; Xu, Xiangru; Grizzle, Jessy W. IEEE Transactions on Automatic Control, Vol. 62, Issue 8 https://doi.org/10.1109/TAC.2016.2638961	journal	August 2017
Fixed-Time Nash Equilibrium Seeking in Time-Varying Networks Poveda, Jorge I.; Krstić, Miroslav; Başar, Tamer IEEE Transactions on Automatic Control, Vol. 68, Issue 4 https://doi.org/10.1109/TAC.2022.3168527	journal	April 2023
Inverse Optimal Safety Filters Krstic, Miroslav IEEE Transactions on Automatic Control, Vol. 69, Issue 1 https://doi.org/10.1109/TAC.2023.3278788	journal	January 2024
Prescribed-Time Safety Design for Strict-Feedback Nonlinear Systems Abel, Imoleayo; Steeves, Drew; Krstić, Miroslav IEEE Transactions on Automatic Control, Vol. 69, Issue 3 https://doi.org/10.1109/TAC.2023.3326393	journal	March 2024
Safety-Critical Control With Input Delay in Dynamic Environment Molnar, Tamas G.; Kiss, Adam K.; Ames, Aaron D. IEEE Transactions on Control Systems Technology, Vol. 31, Issue 4 https://doi.org/10.1109/TCST.2022.3227451	journal	July 2023
Experimental Safe Extremum Seeking for Accelerators Williams, Alan; Scheinker, Alexander; Huang, En-Chuan IEEE Transactions on Control Systems Technology https://doi.org/10.1109/TCST.2024.3377828	journal	January 2024
Safety Barrier Certificates for Collisions-Free Multirobot Systems Wang, Li; Ames, Aaron D.; Egerstedt, Magnus IEEE Transactions on Robotics, Vol. 33, Issue 3 https://doi.org/10.1109/TRO.2017.2659727	journal	June 2017
Control-Barrier-Function-Based Design of Gradient Flows for Constrained Nonlinear Programming Allibhoy, Ahmed; Cortés, Jorge IEEE Transactions on Automatic Control, Vol. 69, Issue 6 https://doi.org/10.1109/tac.2023.3306492	journal	June 2024
Continuous-Time Zeroth-Order Dynamics with Projection Maps: Model-Free Feedback Optimization with Safety Guarantees Chen, Xin; Poveda, Jorge I.; Li, Na IEEE Transactions on Automatic Control https://doi.org/10.1109/tac.2025.3537956	journal	January 2025
Optimization and Nonsmooth Analysis Clarke, Frank H. Classics in Applied Mathematics https://doi.org/10.1137/1.9781611971309	book	January 1990
Driver Intent Prediction with Barrier Functions Rahman, Yousaf; Jankovic, Mrdjan; Santillo, Mario 2021 American Control Conference (ACC) https://doi.org/10.23919/ACC50511.2021.9483393	conference	May 2021
On Non-Local Stability Properties of Extremum Seeking Control Tan, Y.; Nešić, D.; Mareels, I. M. Y. IFAC Proceedings Volumes, Vol. 38, Issue 1 https://doi.org/10.3182/20050703-6-CZ-1902.00747	journal	January 2005
Constructive Safety Using Control Barrier Functions Wieland, Peter; Allgöwer, Frank IFAC Proceedings Volumes, Vol. 40, Issue 12 https://doi.org/10.3182/20070822-3-za-2920.00076	journal	January 2007
Saddle Point Seeking for Convex Optimization Problems Dürr, Hans-Bernd; Zeng, Chen; Ebenbauer, Christian IFAC Proceedings Volumes, Vol. 46, Issue 23 https://doi.org/10.3182/20130904-3-FR-2041.00023	journal	January 2013

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Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

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