Finite-time asynchronous state estimation for jump systems with partial transition probabilities via redundant channels: A co-design method

• Published in: Journal of the Franklin Institute Vol. 358; no. 18; pp. 10095 - 10120
• Main Authors: Chen, Haiyang, Gao, Fangzheng
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.12.2021; Elsevier Science Ltd
• Subjects: Asynchronous; Co-design; Estimating techniques; H infinity; Markov analysis; Markov chains; Matrix; Probability; Robot arms; State estimation; Transition probabilities
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.09.032

•The impact of synchronous degree on estimation is constrained by the known degree.•The proposed model enlarges the feasible domain and minifies the upper bound of error.•Finite-time H∞ asynchronous state estimators are devised with new redundant channels.•An iterative-algorithm-based approach is developed to decouple nonlinear terms. This paper addresses the H∞ finite-time asynchronous state estimation issue for Markov jump systems with partial transition probabilities. A hidden-Markov-chain-based redundant channel model (HMCb-RCM) is established to reflect a more practical situation. Based on the output of the HMCb-RCM, firstly an asynchronous full-order state estimator is devised for the jump system with partial transition probabilities. Then, new sufficient criteria are derived such that the state estimation error is H∞ stochastically finite-time bounded. The relationship between the partial transition probabilities and asynchronous modes is revealed as few attempts. The conditional transition probability matrix (CTPM) for the HMCb-RCM is not fixed but designable accordingly; a co-design strategy is newly developed to synthesize the CTPM and the state estimator simultaneously, which produces less conservatism than that with fixed CTPM. Finally, the theoretical results are applied to a one-link robotic manipulator to validate the proposed results.