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This paper proposes a semidefinite programming based method for estimatingmoments of a stochastic hybrid system (SHS). For polynomial SHSs -- whichconsist of polynomial continuous vector fields, reset maps, and transitionintensities -- the dynamics of moments evolve according to a system of linearordinary differential equations. However, it is generally not possible to solvethe system exactly since time evolution of a specific moment may depend uponmoments of order higher than it. One way to overcome this problem is to employso-called moment closure methods that give point approximations to moments, butthese are limited in that accuracy of the estimations is unknown. We find lowerand upper bounds on a moment of interest via a semidefinite program thatincludes linear constraints obtained from moment dynamics, along withsemidefinite constraints that arise from the non-negativity of moment matrices.These bounds are further shown to improve as the size of semidefinite programis increased. The key insight in the method is a reduction from stochastichybrid systems with multiple discrete modes to a single-mode hybrid system withalgebraic constraints. We further extend the scope of the proposed method to aclass of non-polynomial SHSs which can be recast to polynomial SHSs viaaugmentation of additional states. Finally, we illustrate the applicability ofresults via examples of SHSs drawn from different disciplines.

Moment Analysis of Stochastic Hybrid Systems Using Semidefinite Programming