The construction of the program control with probability one for stochastic dynamic systems with jumps

TL;DR

This paper develops a method to construct control programs with probability one for stochastic nonlinear systems with jumps, ensuring the system follows a desired trajectory using algebraic solutions based on first integral theory.

Contribution

It introduces a novel algorithm for designing control programs with probability one for systems with Wiener and Poisson perturbations, based on first integral theory.

Findings

Control programs with probability one are achievable for systems with jumps.

The control design reduces to solving algebraic linear equations.

The method ensures the system follows the prescribed trajectory almost surely.

Abstract

Investigate the stochastic dynamic non-linear system with the Wiener and the Poisson perturbations. For such systems we construct the program control with probability one, which allows this system to move on the given trajectory. In this case the control program is solution of the algebraic system of linear equations. Considered algorithm is based on the first integral theory for stochastic differential equations system.