ℋ2 filter design through multi-simplex modeling for discrete-time Markov jump linear systems with partly unknown transition probability matrix

2014 ◽  
Author(s):  
Cecilia F. Morais ◽  
Marcio F. Braga ◽  
Marcio J. Lacerda ◽  
Ricardo C. L. F. Oliveira ◽  
Pedro L. D. Peres
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump Linear Systems

Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

2021 ◽  
Author(s):  
Jin Zhu ◽  
Kai Xia ◽  
Geir E Dullerud
Keyword(s):  
Linear Systems ◽  
Controller Design ◽  
Hidden Markov ◽  
Transition Probability ◽  
Original System ◽  
Transition Probability Matrix ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Weighting Matrix ◽  
Markov Jump Linear Systems

Abstract This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

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