Moment analysis of stochastic hybrid systems using semidefinite programming

Khem Raj Ghusinga, Andrew Lamperski, Abhyudai Singh

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Abstract

This paper proposes a method based on semidefinite programming for estimating moments of stochastic hybrid systems (SHSs). The class of SHSs considered herein consists of a finite number of discrete states and a continuous state whose dynamics as well as the reset maps and transition intensities are polynomial in the continuous state. For these SHSs, the dynamics of moments evolve according to a system of linear ordinary differential equations. However, it is generally not possible to exactly solve the system since time evolution of a specific moment may depend upon moments of order higher than it. Our methodology recasts an SHS with multiple discrete modes to a single-mode SHS with algebraic constraints. We then find lower and upper bounds on a moment of interest via a semidefinite program that includes linear constraints obtained from moment dynamics and those arising from the recasting process, along with semidefinite constraints coming from the non-negativity of moment matrices. We illustrate the methodology via an example of SHS.

Original languageEnglish (US)
Article number108634
JournalAutomatica
Volume112
DOIs
StatePublished - Feb 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Ltd

Keywords

  • Convex programming
  • Jump process
  • Optimization
  • Polynomial models
  • Stochastic systems

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