research-article

Piece-wise analytic trajectory computation for polytopic switching between stable affine systems

Author:

Maben RabiAuthors Info & Claims

HSCC '20: Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control

Article No.: 5, Pages 1 - 11

https://doi.org/10.1145/3365365.3382204

Published: 22 April 2020 Publication History

Abstract

Our problem is to compute trajectories of a hybrid system that switches between stable affine ODEs, with switching triggered by hyperplane crossings. Instead of integrating over relatively short time steps, we propose to analytically calculate the affine ODE trajectories between switching times. Our algorithm computes the switching times themselves by Chebyshev interpolation of the analytic trajectory pieces, and polynomial root finding. We shrink the interpolation time intervals using bounds on the times needed by the affine ODE trajectories to enter certain Lyapunov sub-level sets. Based on the Chebfun package, we give a MATLAB implementation of our algorithm. We find that this implementation simulates Relay feedback systems as accurately and sometimes faster than conventional algorithms.

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Cited By

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
Berger GRabi M(2021)Bounds on set exit times of affine systems, using Linear Matrix InequalitiesIFAC-PapersOnLine10.1016/j.ifacol.2021.08.51254:5(283-288)Online publication date: 2021
https://doi.org/10.1016/j.ifacol.2021.08.512

Index Terms

Piece-wise analytic trajectory computation for polytopic switching between stable affine systems
1. Computing methodologies
  1. Modeling and simulation
    1. Simulation theory
      1. Systems theory
    2. Simulation types and techniques
      1. Continuous models
2. Mathematics of computing
  1. Mathematical software
    1. Solvers

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cover image ACM Conferences

HSCC '20: Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control

April 2020

324 pages

ISBN:9781450370189

DOI:10.1145/3365365

Program Chairs:
Aaron Ames
California Institute of Technology
,
Sanjit A. Seshia
University of California, Berkeley
,
Publications Chair:
Jyotirmoy Deshmukh
University of Southern California

Copyright © 2020 ACM.

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Publication History

Published: 22 April 2020

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European Commission

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HSCC '20

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SIGBED

HSCC '20: 23rd ACM International Conference on Hybrid Systems: Computation and Control

April 22 - 24, 2020

New South Wales, Sydney, Australia

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Cited By

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
Berger GRabi M(2021)Bounds on set exit times of affine systems, using Linear Matrix InequalitiesIFAC-PapersOnLine10.1016/j.ifacol.2021.08.51254:5(283-288)Online publication date: 2021
https://doi.org/10.1016/j.ifacol.2021.08.512

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