On Problem Of The Decentralized Model Reference Adaptive Control For The Large-Scale Systems

With the continuous progress of human society, the system scale enlarges, and its structure changes variously and complexly. As this large-scale systems has some characteristics like high dimensional and large-scaled, the theory of it has become a specialized research field. For the large-scale systems, a centralized way of control will result in complexity of information exchange through the whole large-scale system. And it not only leads to high cost of operation, but also leads to lower reliability of the system. Taking the system's reliability and its economy into consideration, we began to use the decentralized control to deal with controlling issues for the complex large-scale systems since 1970s.As a more mature adaptive control systems, model reference adaptive control systems has a wide range of applications in the actual system. Many scholars have studied decentralized model reference adaptive control for large-scale system, but the choice of reference model is lack of interconnection items. The role of interconnection items is extremely important, it influents the overall performance of large-scale systems. Though a few scholars add interconnection items to the reference model, the reference model's interconnected matrix and adjustable system's interconnected matrix are coherent. This article is based on the problem, and offering an opinion that when the reference model's interconnected matrix and adjustable system's interconnected matrix are inconsistent, we should carry on the decentralized adaptive model-following reference control for the time-delay large-scale systems firstly. Secondly, in the actual system, on one hand, due to the existence of various factors such as modeling error, measurement error and unpredictable external disturbances, the system model will have inevitable uncertainties; On the other hand, the time-delay maybe happen in many practical engineering systems such as electrical systems, irrigation systems, networked control systems, and the delay characteristics may result in system instability or performance degradation of the dynamic response. In view of it, this article add the interconnected terms to the reference model, and we should carry on the decentralized model reference adaptive control for two classes of uncertain time-delay large-scale systems.In this paper, we mainly use the tools of matrix analysis and linear matrix inequalities, the methods of decentralized control and model reference adaptive control, and based on Lyapunov stability theory to study the three classes of decentralized model reference adaptive control problem. The main contents of this article are as follows:(1) A brief summary of the complex large-scale systems and the adaptive control systems.(2) The problem of decentralized adaptive model-following reference control for a class of time-delay large-scale systems is studied. When choosing reference model, we consider the interaction between the subsystem, give the expectations of interconnected matrix in the interconnection items. Besides, when the reference model system's interconnected matrix and adjustable system's interconnected matrix are inconsistent, the decentralized adaptive control law is given and asymptotic stability of the whole large-scale systems is proved by means of Lyapunov stability theory.(3) After the problem of decentralized model reference adaptive control for two classes of uncertain time-delay large-scale systems are studied, we find out that one problem is decentralized model reference adaptive control for uncertain time-delay large-scale system with time-varying exterior disturbance, and the other problem is decentralized model reference adaptive control for uncertain time-delay large-scale systems with parametric perturbation. When choosing reference model, we consider the interaction between the subsystem, give the expectations of interconnected matrix in the interconnection items. The decentralized adaptive control law is given and uniformly ultimately bounded of two classes of uncertain time-delay large-scale systems is proved by means of Lyapunov stability theory.