Model Predictive Control For Markov Jump Systems

With the development of automatic control technology,the system structure is becoming more and more complex,and it has become difficult to describe their change rules by a single dynamic equation.As a special class of hybrid systems,Markov jump systems have been widely favored by academia and industry because of their simple mathematical description and powerful modelling capability for real systems.Markov jump systems are often subject to physical,economic,and performance constraints of themselves,and traditional control methods seem to be stretched in face of these problems.Model Predictive Control(MPC),as advanced control technology,is a valuable research topic based on Markov jump systems due to its unique optimization mechanism on the receding horizon and its ability to deal with constraints.However,the traditional fully online MPC algorithm has been greatly impacted in terms of computational complexity with the increasing size of the controlled objects and the changing jump rules.The potential value created by time cost is increasingly attached importance in the pursuit of economic efficiency.In addition,Markov jump linear systems have encountered obstacles in the process of modelling.The application environment of the system is developing in networking so that the controller cannot fully obtain the effective information of the system,and some systems cannot be completely linearized.These significant difficulties constitute the main motivation for the research.Specifically,the research in this thesis is focused on the following:For the Markov jump system with networked signal transmission control,the Round-Robin protocol is used to network schedule the control inputs,which can effectively reduce the frequency of data communication and the utilization of networks with limited bandwidth.In the cases of imperfect known transition probability information,an upper bound for the "min-max" performance index on the infinite horizon optimization problem is obtained using invariant set theory and matrix inequality techniques.By solving an auxiliary online optimization problem,the explicit expressions mixed-mode-and-token-dependent controllers are obtained,and the recursive feasibility of the problem and the mean-square stability of the closed-loop system is guaranteed.On the other hand,considering the phenomenon that the mode information is not synchronized between the system and the controller in the networked system,the hidden Markov model with partially known detection probability is used to describe.It was noted that the control input is difficult to accurately act on the physical system after transmission through the network,a resilient asynchronous controller with norm bounded uncertain gain is designed by using robust MPC method.By stochastic analysis technology,sufficient conditions to satisfy the requirements of a terminal invariant set are derived,and an online algorithm for solving the controller is designed.As the Markov jump system is a hybrid system with multiple modes,the excessive computational burden is a problem worthy of attention when using the MPC method in an online way.For this reason,a co-design scheme for Markov jump systems with uncontrollable by single-state feedback is presented in an effective MPC framework,and the system transition probability matrix and controller are designed and mean-squared stability is ensured.A finite number of perturbation sequences steers the system state belonging to the initial feasible region into the terminal constraint set within the pre-determined steps.The off-line optimization problem is solved in the terminal constraint set,the mode-dependent feedback control gain and jump rules are co-designed,and the augmented state is used to expand the range of the feasible region.The perturbation is determined by solving the online optimization problem.On the other hand,an efficient MPC scheme is investigated for a class of Markov jump systems with Lur’e nonlinear terms.A novel composite controller is constructed,which the control gain is composed of a combination of linear and non-linear parts.In addition,the controller also contains additional perturbations.Sufficient conditions for the mean-square stability of the closed-loop system are obtained by using the stochastic Lur’e-type Lyapunov function and the Lur’e-type invariant set method.To further reduce online computation and expand the initial feasible region,while ensuring good terminal control performance.The asynchronous controller is designed for Markov jump systems with the MPC problem based on optimizing prediction dynamics.The problem of the finite number of perturbations is solved to establish predictive dynamics to obtain perturbations.The highly coupled inequalities are decoupled by matrix decomposition,Bayes theory,and inequality techniques,and the explicit expressions for the feedback control gains and estimator gains are obtained.The dynamic controller states are designed online and sufficient conditions are driven to prove the feasibility of the algorithm and stability for a close loop system.On the other hand,the MPC problem under imperfect premise matching employing optimizing prediction dynamics is concerned for a class of discrete-time Takagi-Sugeno fuzzy Markov jump systems.Due to the use of imperfect matched premise variable fuzzy controller structure,the technology of optimizing predictive dynamics can effectively reduce the potential computational burden.At the same time,techniques such as matrix factorization and variable substitution are used to solve multiple auxiliary optimization problems to design the controller.It is proved that the system can be mean-square stable under the action of the controller.