A hybrid system is a dynamic system that exhibits both continuous and discrete dynamicbehaviour. In modern engineering field, the systems such as power systems, economicsystems can be modelled as hybrid systems. Such systems are different from conventionallinear systems. The dynamic behaviour, parameters and structural changes caused by theabrupt phenomena can be well described by the stochastic mode system. The feature ofstochastic mode system is that the switching from one mode to another is driven by astochastic process such as Markov chain. The controller, filter design of this type of systemhas been well investigated in the literature. However, different forms of constraints areencountered in the practice such as the physical limit and the safety constraints of the states.On the other hand, the disturbance is inevitable in practice, which leads to worse performanceof the controller. What's more, it may cause the unstability of the system. Thus, it is necessaryand a challenge to study the problem of the controller design and disturbance rejection ofstochastic jump system. The paper mainly focuses on a class of multi-mode system driven bya Markov process (also called Markov jump system), in which the analysis is based on thetransition probability matrix. By applying the method of model predictive control which canexplicitly handle the constraints and invariant sets, the problem of controller design anddisturbance rejection has been well studied. Specifically, the main work is summarized asbelow:1) For the popular nonhomogeneous transition probability matrix which is widely occurred inengineering such as dropouts in NCS, the paper investigates the polyhedron nonhomogeneouscase, the predictive controller is designed. Furthermore, the asymmetric constraints case isconsidered and the initial feasible region is enlarged.2) The chapter mainly focused on how to reduce the on-line computation of stochastic jumpsystem subject to constraints. An offline algorithm is applied, which is a suboptimal algorithm.The algorithm drops the optimal performance to obtain the reduction of computation time andthe dynamic performance is still acceptable. The topic shows the trade-off between time andperformance, optimal performance and suboptimal performance.3) Based on the previous results, the controller design problem for a class of constrainedstochastic jump system with Truncated Gaussian distribution is investigated. The main idea isapplying differential inclusion to include the nonlinearity to avoid solving the complicatednonlinear optimization problem and then make it easier to design the controller.4) Under the bounded disturbance, the disturbance rejection problem of three casesnonhomogeneous, partly unknown and Truncated Gaussian distribution are respectively studied. The aim is to regulate the system output in a certain area or make the system stable insuch a small area including the origin and thus the influence of the disturbance is suppressed.5) Finally, the final Chapter summarizes the whole work of the paper and give the furtherdirection. |