Decentralized Robust Predictive Control For Uncertain Large-scale System With Convex Polyhedral Description

In the process of practical engineering, large scale and complicated structure systems are visible everywhere, such as electric power systems, aerospace systems, large-scale space structure systems etc. Due to the centralized control will make the exchange of information of the whole control very complex, we adopt the distributed control for the large-scale systems. For the large complex system, decentralized structure can solve the real-time problem of the predictive control of high dimensional systems, and the predictive control can solve the uncertain factors of the model. So we make a complementary combination of decentralized control and predictive control, then we can get the decentralized predictive control. It is an effective method to solve the control problems in large scale systems. In this paper, based on the convex polyhedron description of the large-scale systems, we study the decentralized robust predictive control problem by using the LMI method and the Lyapunov stability theory. The main contents of this paper are given as follows:Firstly, we introduce the background and significance of the topic and describe the basic principle and the development of predictive control in detail. Then we introduce the robust predictive control and its development status. Specially, we introduce the research status of the robust predictive control for the convex polyhedron systems.Secondly, we introduce two kinds of the model uncertainty description. Then we introduce the related knowledge of linear matrix inequalities. In particular, we introduced a lemma and how to use it to transform the nonlinear matrix inequality into a linear matrix inequality.Lastly, when the system states are unmeasurable, the problem of decentralized robust predictive control with output feedback is studied for convex polyhedral uncertain large-scale system. By constructing the Lyapunov function and with the use of the idea of variable transformation and LMI methods, the infinite time domain "min-max" optimization problems are converted into convex programming problems. The sufficient conditions for the existence of this controller are derived. The controller enables the closed-loop large-scale systems robust stable. A simulation example shows the effectiveness of the control algorithm.