p-Safe analysis of stochastic hybrid processes

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Wisniewski, Rafael and Bujorianu, Manuela L. and Sloth, Christoffer (2020) p-Safe analysis of stochastic hybrid processes. IEEE Transactions on Automatic Control, 65 (12). pp. 5220-5235. ISSN 0018-9286 (https://doi.org/10.1109/TAC.2020.2972789)

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Abstract

We develop a method for determining whether a stochastic system is safe, i.e., whether its trajectories reach unsafe states. Specifically, we define and solve a probabilistic safety problem for Markov processes. Based on the knowledge of the extended generator, we are able to develop an evolution equation, as a system of integral equations, describing the connection between unsafe and initial states. Subsequently, using the moment method, we approximate the infinite-dimensional optimization problem searching for the largest set of safe states by a finite-dimensional polynomial optimization problem. In particular, we address the above safety problem to a special class of stochastic hybrid processes, namely piecewise-deterministic Markov processes. These are characterized by deterministic dynamics and stochastic jumps, where both the time and the destination of the jumps are stochastic. In addition, the jumps can be both spontaneous (in the style of a Poisson process) and forced (governed by guards). In this case, the extended generator of this process and its corresponding martingale problem turn out to be defined on a rather restricted domain. To circumvent this difficulty, we bring the generalized differential formula of this process into the evolution equation and, subsequently, formulate a polynomial optimization.

  • Item type:Article
    ID code:72932
    Dates:
    Date
    Event
    31 December 2020
    Published
    10 February 2020
    Published Online
    22 January 2020
    Accepted
    Notes:© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    Subjects:Technology > Hydraulic engineering. Ocean engineering
    Department:Faculty of Engineering > Naval Architecture, Ocean & Marine Engineering
    Depositing user: Pure Administrator
    Date deposited:25 Jun 2020 13:53
    Last modified:11 Nov 2024 12:44
    URI:https://strathprints.strath.ac.uk/id/eprint/72932
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