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Mode feedback control strategy for continuous‐time Markovian jump linear systems with controllable mode transition rate matrix
Author(s) -
Chen Wei,
Zhu Jin
Publication year - 2018
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2465
Subject(s) - control theory (sociology) , mode (computer interface) , transition rate matrix , controller (irrigation) , stability (learning theory) , jump , computer science , state (computer science) , feedback control , full state feedback , control (management) , control engineering , mathematics , engineering , algorithm , statistics , physics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology , operating system
Summary This paper investigates mode feedback control strategy for continuous‐time Markovian jump linear systems with controllable mode transition rate matrix (MTRM). Based on the fact that system stability as well as its performance is dependent on MTRM, a mode feedback controller is proposed to perform control on MTRM such that system stability is achieved. Meanwhile, this strategy can help to improve system performance since it can adjust the occurrence probability of each subsystem. Firstly, taking into account that MTRM will totally determine system stability in absence of state feedback controller, the existence and restrictions on mode feedback controller are discussed where two cases are included. Then, based on a quadratic stabilization cost function that is a combination of state cost and control cost, a feasible solution of mode feedback control strategy is then obtained with its detailed algorithm given. Simulation results including comparisons with current state feedback mechanism are provided to illustrate the effectiveness of the proposed strategy.