Stabilization of Stochastic Dynamical Systems of a Random Structure with Markov Switches and Poisson Perturbations

Taras Lukashiv (), Yuliia Litvinchuk, Igor V. Malyk, Anna Golebiewska and Petr V. Nazarov ()
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Taras Lukashiv: Multiomics Data Science Research Group, Department of Cancer Research, Luxembourg Institute of Health, L-1445 Strassen, Luxembourg
Yuliia Litvinchuk: Department of Mathematical Problems of Control and Cybernetics, Yuriy Fedkovych Chernivtsi National University, 58000 Chernivtsi, Ukraine
Igor V. Malyk: Department of Mathematical Problems of Control and Cybernetics, Yuriy Fedkovych Chernivtsi National University, 58000 Chernivtsi, Ukraine
Anna Golebiewska: NORLUX Neuro-Oncology Laboratory, Department of Cancer Research, Luxembourg Institute of Health, L-1210 Luxembourg, Luxembourg
Petr V. Nazarov: Multiomics Data Science Research Group, Department of Cancer Research, Luxembourg Institute of Health, L-1445 Strassen, Luxembourg

Mathematics, 2023, vol. 11, issue 3, 1-22

Abstract: An optimal control for a dynamical system optimizes a certain objective function. Here, we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the system stable in probability. Sufficient conditions of the stability in probability are obtained, using the second Lyapunov method, in which the construction of the corresponding functions plays an important role. Here, we provide a solution to the problem of optimal stabilization in a general case. For a linear system with a quadratic quality function, we give a method of synthesis of optimal control based on the solution of Riccati equations. Finally, in an autonomous case, a system of differential equations was constructed to obtain unknown matrices that are used for the construction of an optimal control. The method using a small parameter is justified for the algorithmic search of an optimal control. This approach brings a novel solution to the problem of optimal stabilization for a stochastic dynamical system with a random structure, Markov switches and Poisson perturbations.

Keywords: optimal control; Lyapunov function; system of stochastic differential equations; Markov switches; Poisson perturbations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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