Receding Horizon $\mathbf{H}_{\infty}$ Control of Hidden Markov Jump Linear Systems

2018 ◽  
Author(s):  
Scott B. Gibson ◽  
Daniel J. Stilwell
Keyword(s):  
Linear Systems ◽  
Hidden Markov ◽  
Receding Horizon ◽  
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.

Receding Horizon Control for Uncertain Markov Jump Linear Systems with Time Delay and Actuator Saturation

2013 ◽  
Vol 303-306 ◽  
pp. 1193-1199 ◽  
Author(s):  
Ji Wei Wen
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Actuator Saturation ◽  
Receding Horizon Control ◽  
Receding Horizon ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Current Time ◽  
Mean Square Stability ◽  
Markov Jump Linear Systems

A robust receding horizon control (RHC) scheme is developed for uncertain discrete-time Markov Jump Linear Systems (MJLS) with time delay and actuator saturation where the system uncertainties and jumping transition probabilities are assumed to belong to some convex sets. Firstly, when time delay is considered, a sufficient condition of minimizing upper bound of the cost function and mean square stability of the closed-loop system are established based on the Lyapunov Krasovskii function which depend on the current time jump mode. At each sampling time, an optimal control gain can be obtained by solving the semi-definite programming (SDP) problem. Then, the proposed strategy is extended to design robust RHC scheme for uncertain MJLS with both time delay and actuator saturation. Moreover, the domain of attraction can be estimated through a modified invariant ellipsoid. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Stable receding-horizon scenario predictive control for Markov-jump linear systems

Automatica ◽  
2017 ◽  
Vol 86 ◽  
pp. 121-128 ◽  
Author(s):  
Antonio Sala ◽  
Manuel Hernández-Mejías ◽  
Carlos Ariño
Keyword(s):  
Linear Systems ◽  
Predictive Control ◽  
Receding Horizon ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump Linear Systems
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