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Moment analysis of stochastic hybrid systems using semidefinite programming. (English) Zbl 1430.93199

Summary: 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.

MSC:

93E03 Stochastic systems in control theory (general)
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C15 Control/observation systems governed by ordinary differential equations
90C22 Semidefinite programming

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References:

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