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Optimal control for infinite-dimensional linear systems with Markovian jumps in Borel spaces

Year: 2025

Type: article

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.

Source: DOAJ (DOAJ: Directory of Open Access Journals)

Authors: Viorica Mariela Ungureanu, Iulia Iarina Ungureanu

Institutions: Constantin Brâncuși University of Targu Jiu, Technical University of Cluj-Napoca

Language: English

Topic: Stability and Control of Uncertain Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7033133612

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