15th International Asian School-Seminar "Optimization Problems of complex systems", 26-30 August 2019.

Novosibirsk, Russia

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Khrustalev M.M.   Tsarkov K.A.  

Terminal Invariance Sufficient Conditions for Jump Stochastic Systems

Reporter: Tsarkov K.A.

In this work, we present conditions of terminal invariance for dynamical stochastic piecewise continuous controllable processes. The processes under consideration are described by nonlinear differential equation systems containing a stochastic jump component in the form of the integral over Poisson random measure as well as a deterministic continuous part in the right hand side. We assume that the measure parameters (intensity and jump values distribution) may change over time. The initial condition is fixed. Terminal invariance means that the given functional (terminal criterion) takes a constant value with probability 1. Here we formulate sufficient conditions of terminal invariance, which allow us to calculate this value explicitly. The scheme of conditions usage is demonstrated in the model example. Within the example we show the key properties of terminal invariant control strategy allowing the system to parry any possible realization of the random jump process.