Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Optimal Control of Discrete Time-varying System with Multiple Delays and Multiplicative Noises

Version 1 : Received: 16 May 2023 / Approved: 18 May 2023 / Online: 18 May 2023 (10:32:41 CEST)

How to cite: Zhang, Q.; Sheng, C.; Lu, X.; Wang, H. Optimal Control of Discrete Time-varying System with Multiple Delays and Multiplicative Noises. Preprints 2023, 2023051330. https://doi.org/10.20944/preprints202305.1330.v1 Zhang, Q.; Sheng, C.; Lu, X.; Wang, H. Optimal Control of Discrete Time-varying System with Multiple Delays and Multiplicative Noises. Preprints 2023, 2023051330. https://doi.org/10.20944/preprints202305.1330.v1

Abstract

This paper is concerned with the optimal linear quadratic Gaussian (LQG) control problem for discrete time-varying system with multiple input delays and multiplicative noises. The main contributions are two-fold. Firstly, when the state variables can be observed exactly, we obtain a necessary and suffcient condition for the multiple-delays system in terms of the non-homogeneous relationship between the state and costate, which is the solution to the coupled forward and backward stochastic difference equations. Secondly, when the state variables are partially observed, we derive a suboptimal linear output feedback controller for the discrete-time system based on the obtained results of the optimal LQG control. Numerical examples are shown to illustrate the proposed algorithm.

Keywords

LQG control; multiple delays; discrete time-varying system; multiplicative noises

Subject

Computer Science and Mathematics, Applied Mathematics

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