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. Preprints2023, 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
Zhang, Q.; Sheng, C.; Lu, X.; Wang, H. Optimal Control of Discrete Time-varying System with Multiple Delays and Multiplicative Noises. Preprints2023, 2023051330. https://doi.org/10.20944/preprints202305.1330.v1
APA Style
Zhang, Q., Sheng, C., Lu, X., & Wang, H. (2023). Optimal Control of Discrete Time-varying System with Multiple Delays and Multiplicative Noises. Preprints. https://doi.org/10.20944/preprints202305.1330.v1
Chicago/Turabian Style
Zhang, Q., Xiao Lu and Haixia Wang. 2023 "Optimal Control of Discrete Time-varying System with Multiple Delays and Multiplicative Noises" Preprints. 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.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.