Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 20 (2025), 173 -- 192

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OPTIMAL CONTROL FOR INFINITE-DIMENSIONAL LINEAR SYSTEMS WITH MARKOVIAN JUMPS IN BOREL SPACES

Viorica Mariela Ungureanu and Iulia Iarina Ungureanu

Abstract. This paper addresses an optimal control problem for discrete-time, infinite - dimensional linear systems with Markovian jumps (LSMJs) in a Borel space. The main objective is to minimize an infinite-horizon, non-negative quadratic cost functional for time-dependent LSMJs by generalizing previous findings on finite - dimensional systems to the infinite-dimensional case. A second objective is to establish a framework that extends known results concerning the existence of certain global solutions (such as minimal, maximal, and stabilizing solutions) for a more general class of Riccati equations associated with the optimal control problem. Key results include the convergence properties of the zero-final-value solutions of the associated backward generalized Riccati equations (GREs) and Lyapunov-type stability criteria for LSMJs. The optimal control law and the corresponding optimal cost are then computed using the minimal solution of the GRE.

2020 Mathematics Subject Classification: 93C05; 93C55; 49N10; 60J75; 47J35
Keywords: optimal control; infinite-dimensional systems; Markovian jump systems; generalized Riccati equation; linear-quadratic regulator

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V.M. Ungureanu
Department of Energy, Environment and Agritourism,
Constantin Brancusi University of Targu Jiu,
30 Eroilor Street, 210135, Tg-Jiu, Gorj, Romania.
e-mail: lvungureanu@yahoo.com



I.I. Ungureanu
Department of Computers Science,
Technical University of Cluj-Napoca,
26-28 G. Baritiu Street, 400027 Cluj-Napoca, Romania.
e-mail: iarina.ungureanu@gmail.com

https://www.utgjiu.ro/math/sma