Observer-Based Model Reference Tracking Control of the Markov Jump System with Partly Unknown Transition Rates
Abstract
:1. Introduction
2. Problem Description and Preliminaries
3. Observer and Control Law Design
3.1. Observer Design
(1), | (2), |
(3), | (4), |
(5), | (6). |
3.2. Control Law Design
4. Parameter Solutions
4.1. State Feedback Control Law Design
4.2. Feedforward Control Law Design
4.3. Algorithm for Solving the Controller
- According to Theorem 2, compute the state feedback gain matrix.
- Judge whether the matrix pair is controllable. If it is controllable, solve Lemma 3, and go on to the next step; otherwise, the feedforward compensator does not exist.
- Compute and based on Lemma 4, then compute the gain matrix of the feedforward compensator.
5. Numerical Example
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
(1), | (2), |
(3), | (4), |
(5), | (6), |
(7), | (8). |
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Song, W.; Jin, A. Observer-Based Model Reference Tracking Control of the Markov Jump System with Partly Unknown Transition Rates. Appl. Sci. 2023, 13, 914. https://doi.org/10.3390/app13020914
Song W, Jin A. Observer-Based Model Reference Tracking Control of the Markov Jump System with Partly Unknown Transition Rates. Applied Sciences. 2023; 13(2):914. https://doi.org/10.3390/app13020914
Chicago/Turabian StyleSong, Weiqiang, and Aijuan Jin. 2023. "Observer-Based Model Reference Tracking Control of the Markov Jump System with Partly Unknown Transition Rates" Applied Sciences 13, no. 2: 914. https://doi.org/10.3390/app13020914
APA StyleSong, W., & Jin, A. (2023). Observer-Based Model Reference Tracking Control of the Markov Jump System with Partly Unknown Transition Rates. Applied Sciences, 13(2), 914. https://doi.org/10.3390/app13020914