Finite Frequency Predictive Control For Markov Jump Systems

An important and challenging subject in the control theory of Markov jump system is to obtain the systematic method of its constrained controller design,and realize the optimization of performance index,the feasibility of control algorithm and the mean square stability of closed-loop system.For the constraint and optimal control of jump systems,the predictive control strategy has attracted the most attention.When using the jump system model to solve complex industrial problems,if the finite frequency information of noise energy can be further combined,the performance optimization effect and the anti-interference ability of the system may be improved at the same time.This paper systematically studies the finite band predictive control of Markov jump system,taking into account performance optimization,anti-interference and resource saving.The main research work of this paper is summarized as follows:1.This chapter aims to study the receding horizon H_∞control problem for Markov jump systems(MJSs)in finite frequency domain,so as to achieve better constrained optimization. First,the augmented system method is used to transform the random jump system with multi-modes into a single mode system embeded with transition probabilities.The dynamic behavior of the augmented random system is characterized by the mathematical expectation of the original system.Second,the frequency information of exogenous noise over a specific frequency band and system input/output constraints were introduced into the controller design.The receding horizon H_∞control is implemented from both the frequency and state space perspectives.The standard semi-definite programming(SDP)is solved online when solving H_∞control gain.Finally,the feasibility of the receding horizon strategy and the mean square stability of the closed-loop MJS is analyzed.2.A self-triggered saturated model predictive control(SMPC)for Markov jump system(MJS) is studied in finite-frequency domain.Its main purpose is to save communication and computing resources on the premise of ensuring certain control performance.In order to reduce resource occupation,a self-triggering mechanism is designed,which predicts the next triggering time according to the current sampling value and sampling time.Through the convex combinatorial approach,a saturated model predictive control strategy is designed to achieve the desired system dynamics.3.The dynamic output feedback model predictive control of Markov jump system with finite frequency band information is studied,and the co-design is realized in time domain and frequency domain.The multi-objective optimization problem is transformed into a standard SDP problem for solving by a special congruential transformation.The SDP condition greatly reduces the computational effort by eliminating bilinear matrix inequalities or equation constraints in the existing literature.Using the generalized kalman-yakubovc- popov lemma,the H_∞norm of the transfer function is optimized in three different frequency ranges.