The Research Of Feedback Predictive Control For Markov Jump Systems

Markov jump systems have two kinds of mixed dynamic form, a known as the mode,described by the continuous and discrete state Markov process; Another is called the state, bythe state space equation of each mode. We can use stochastic differential equation anddifference equation touniform the two different dynamic, which makes people can use moderncontrol theory and method to analyze and study the Markov jump system.In this paper, Feedback predictive control study for Markov jump system were discussed.Feedback predictive control have two characteristics that combined with feedback control inreal information feedback to the controlled system for real-time control and predictive controlof rolling optimization. By using the thought of optimal control, the invariant set theory andthe linear matrix inequality (LMI), the feedback predictive control for Markov jump system isinnovation significance for the following work:1. In order to overcome the high computational burden online in past state feedback predictivecontrol when solving SDP, on the basis of normal state feedback function, we increase a freevariable, and the feedback law of offline design, free variable is online design, this methodincreased the freedom of design degrees, and adopt the method of off-line comprehensivedesign online, which will reduce the amount of calculation.2. In view of the system state maybe cannot be measured and transition probability are partlyunknown, we put forward a kind of output feedback predictive control strategy based on stateobserver. This method will integrated design controller and observer, considering the systeminput and output constraints, using observation condition to construct the performance index,we get the optimal feedback control laws through optimizing infinite time quadraticperformance index repeated online, and give a set of inequality conditions makes the real state,observation and observation error remains within a ellipse, guaranteeing the convergence ofthe system.3. Consider the design of feedback control law is mostly are directly dependent on the modein previous paper, to some extent, it limits the controller design degrees of freedom, whenMarkov jump system has too many jump modes, the online computation burden of predictivecontrol method is very big, and it is hard to find a feasible solution of optimizationperformance index. So on the basis of guaranteeing the control performance, cycle idea of theinvariant set to Markov jump system feedback predictive control, resulting in a series of notdirectly based on the modes of the feedback control law. Considering the characteristics ofrandom jump Markov jump system, the control strategy is divided into two parts whichcontain offline part and online part. This method increases the design degrees of freedom, anda certain extent, it expands the stabilizable set.