research-article

Robust invariant sets generation for state-constrained perturbed polynomial systems

Authors:

Martin FränzleAuthors Info & Claims

HSCC '19: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

Pages 128 - 137

https://doi.org/10.1145/3302504.3311810

Published: 16 April 2019 Publication History

Abstract

In this paper we study the problem of computing robust invariant sets for state-constrained perturbed polynomial systems within the Hamilton-Jacobi reachability framework. A robust invariant set is a set of states such that every possible trajectory starting from it never violates the given state constraint, irrespective of the actual perturbation. The main contribution of this work is to describe the maximal robust invariant set as the zero level set of the unique Lipschitz-continuous viscosity solution to a Hamilton-Jacobi-Bellman (HJB) equation. The continuity and uniqueness property of the viscosity solution facilitates the use of existing numerical methods to solve the HJB equation for an appropriate number of state variables in order to obtain an approximation of the maximal robust invariant set. We furthermore propose a method based on semi-definite programming to synthesize robust invariant sets. Some illustrative examples demonstrate the performance of our methods.

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Cited By

Yang HWang CBi XIvanov I(2024)Robust Invariance Conditions of Uncertain Linear Discrete Time Systems Based on Semidefinite Programming DualityMathematics10.3390/math1216251212:16(2512)Online publication date: 14-Aug-2024
https://doi.org/10.3390/math12162512
Schafer LAlthoff M(2024)Computing Robust Control Invariant Sets of Nonlinear Systems Using Polynomial Controller Synthesis2024 American Control Conference (ACC)10.23919/ACC60939.2024.10644939(4162-4169)Online publication date: 10-Jul-2024
https://doi.org/10.23919/ACC60939.2024.10644939
Fatnassi WShoukry Y(2024)PolyARBerNN: A Neural Network Guided Solver and Optimizer for Bounded Polynomial InequalitiesACM Transactions on Embedded Computing Systems10.1145/363297023:2(1-26)Online publication date: 24-Jan-2024
https://dl.acm.org/doi/10.1145/3632970
Show More Cited By

Index Terms

Robust invariant sets generation for state-constrained perturbed polynomial systems
1. Security and privacy
  1. Formal methods and theory of security
    1. Logic and verification

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cover image ACM Conferences

HSCC '19: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

April 2019

299 pages

ISBN:9781450362825

DOI:10.1145/3302504

Program Chairs:
Necmiye Ozay
University of Michigan
,
Pavithra Prabhakar
Kansas State University

Copyright © 2019 ACM.

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Published: 16 April 2019

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CAS Pioneer Hundred Talents Program
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HSCC '19: 22nd ACM International Conference on Hybrid Systems: Computation and Control

April 16 - 18, 2019

Quebec, Montreal, Canada

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Overall Acceptance Rate 153 of 373 submissions, 41%

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Cited By

Yang HWang CBi XIvanov I(2024)Robust Invariance Conditions of Uncertain Linear Discrete Time Systems Based on Semidefinite Programming DualityMathematics10.3390/math1216251212:16(2512)Online publication date: 14-Aug-2024
https://doi.org/10.3390/math12162512
Schafer LAlthoff M(2024)Computing Robust Control Invariant Sets of Nonlinear Systems Using Polynomial Controller Synthesis2024 American Control Conference (ACC)10.23919/ACC60939.2024.10644939(4162-4169)Online publication date: 10-Jul-2024
https://doi.org/10.23919/ACC60939.2024.10644939
Fatnassi WShoukry Y(2024)PolyARBerNN: A Neural Network Guided Solver and Optimizer for Bounded Polynomial InequalitiesACM Transactions on Embedded Computing Systems10.1145/363297023:2(1-26)Online publication date: 24-Jan-2024
https://dl.acm.org/doi/10.1145/3632970
Schäfer LGruber FAlthoff M(2024)Scalable Computation of Robust Control Invariant Sets of Nonlinear SystemsIEEE Transactions on Automatic Control10.1109/TAC.2023.327530569:2(755-770)Online publication date: Feb-2024
https://doi.org/10.1109/TAC.2023.3275305
Liao WLiang TWang CYang D(2023)A dimensionality reduction method for computing reachable tubes based on piecewise pseudo-time dependent Hamilton–Jacobi equationApplied Mathematics and Computation10.1016/j.amc.2022.127696441:COnline publication date: 15-Mar-2023
https://dl.acm.org/doi/10.1016/j.amc.2022.127696
Maxim ACaruntu C(2022)Coalitional Distributed Model Predictive Control Strategy for Vehicle Platooning ApplicationsSensors10.3390/s2203099722:3(997)Online publication date: 27-Jan-2022
https://doi.org/10.3390/s22030997
Xue BWang QZhan NFranzle MFeng S(2022)Differential Games Based on Invariant Sets Generation2022 American Control Conference (ACC)10.23919/ACC53348.2022.9867496(1285-1292)Online publication date: 8-Jun-2022
https://doi.org/10.23919/ACC53348.2022.9867496
Xue BZhan N(2022)Robust Invariant Sets Computation for Discrete-Time Perturbed Nonlinear SystemsIEEE Transactions on Automatic Control10.1109/TAC.2021.306331567:2(1053-1060)Online publication date: Feb-2022
https://doi.org/10.1109/TAC.2021.3063315
Cotorruelo AHosseinzadeh MRamirez DLimon DGarone E(2021)Reference dependent invariant setsAutomatica (Journal of IFAC)10.1016/j.automatica.2021.109614129:COnline publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1016/j.automatica.2021.109614
Xue BFranzle MZhan NBogomolov SXia B(2020)Safety Verification for Random Ordinary Differential EquationsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2020.301313539:11(4090-4101)Online publication date: Nov-2020
https://doi.org/10.1109/TCAD.2020.3013135
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