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.
Bibliographical noteFunding Information:
AS is supported by National Science Foundation, USAECCS-1711548. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Debasish Chatterjee under the direction of Editor Daniel Liberzon
- Convex programming
- Jump process
- Polynomial models
- Stochastic systems