Control And Filtering For Two Classes Of Stochastic Jump Systems

Stochastic jump systems have a strong modelling ability for the sudden change of system structures and parameters caused by random factors such as sudden environmental changes,system component failures and data loss,so they have been widely applied to practical fields.Such systems include both general state changes and stochastic mode changes.According to the characteristic of the sojourn-time distribution of the mode,such systems can be divided into Markov jump systems and Semi-Markov jump systems.In this paper,considering uncertainty,input constraints,state constraints,networked transmission failures and asynchronous phenomenon in these two classes of stochastic jump systems,the Lyapunov stability theory,control parametrization method and other methods are used to design the corresponding controllers and filters for Markov jump systems and Semi-Markov jump systems.This paper mainly studies the following aspects.1.Considering discrete-time Markov jump systems with partially unknown transition probabilities and uncertainties,by a probabilistic randomization approach,a probabilistic full order filter is proposed,under which the filtering error system is stochastically stable with a given probability level,and satisfies an 7)2-7)∞performance index.Then,considering the problem that the full order filter cannot be realized due to the high dimension of the system,based on a probabilistic randomization method,a probabilistic reduced-order filter is proposed to ensure that the filtering error system is stochastically stable with a given probability level,and satisfies an ∞ performance index.2.Considering discrete-time Markov jump systems with input constraints,a state feedback controller is designed under the event-triggered mechanism.Based on the Lyapunov stability,ellipsoid invariant set theory and event-triggered conditions,slack matrices are introduced to solve controller gain matrices,so that the closed-loop system state is always in the ellipsoid invariant set and Markov jump systems with input constraints are stochastically stable.Furthermore,considering the suppression of external interference for the system,a design method of event-triggered controller with input constraints satisfying the mixed ∞ and passive performance index is presented.3.For an optimal control problem governed by a continuous-time Markov jump system,considering a linear system,by using derandomization method,the Markov jump system is transformed into a deterministic system with the information of transition rates,and a representative deterministic optimization problem is obtained at the same time.With the aid of the control parametrization method,a parameter selection problem is obtained.By the optimization algorithm based on the gradient,the optimal control law and optimal value of the objective function can be obtained.Then,considering an optimal control problem governed by a nonlinear system,an approximate optimization problem is obtained under the derandomization method and control parametrization method,combined with the transcription technique which can deal with state inequality constraints.Using the optimization algorithm based on the gradient,the optimal control law and optimal value of the objective function are obtained.The state inequality constraints are satisfied.4.Considering the existence of the networked transmission failures,a partially modedependent filter design method is proposed for discrete-time Semi-Markov jump systems.A Bernoulli distribution is used to characterize whether the success of the mode information transmission or not,and achieve the switch between the mode-dependent and mode-independent filters.With the help of the Lyapunov stability theory,SemiMarkov kernel method and ∞ theory,the designed filter can ensure that the filtering error system is -error mean square stable and satisfies an ∞ performance index.The filter gain matrices are obtained through introducing slack matrices.5.Considering the asynchronous phenomenon between Semi-Markov jump system mode and controller mode,an asynchronous control strategy is proposed.The mode of the controller is generated by a conditional probability related to the semi-Markov chain.By using the Lyapunov stability theory and Semi-Markov kernel method,an asynchronous controller is obtained,under which the closed-loop Semi-Markov jump systems are -error mean square stable.The ∞ theory is used to ensure the ability against disturbance.