The Research For The Hadamard Synergic Control

Besides the well known feedback controls, it is also very common for us to control our business by regulating the connections among the subsystems directly in many fields and even in our daily life. For example, such regulating can be found extensively in the quarantine and isolation in epidemics control, power system splitting and etc. In this back-ground, the interconnection structures are considered as one of the most significant factors for the complexity of the systems. The coordination and control of the interconnections become one of the latest and important topics. Hadamard synergic control is a recently pro-posed harmonic control model with the background of emergency control. It is achieved via a composite strategy of the state feedback control and the direct regulation of the part of connection coefficients of system state variables, and may be of perspective applications in complex dynamic network systems and the uniform pre-design techniques for the physical parameters and feedback control. In this dissertation, the fundamental theory is investigated initially for Hadamard synergic control strategy. Some simple applications of this control strategy in the vehicles systems and SARS epidemic control are discussed. The main works are as follows:First, the synergic stabilizability problems are studied. Two types of special undirected networks:star-shaped coupled network and globally coupled network with fixed connection coefficients are investigated. It is pointed out that some subsystems must be unstable for the whole network to be stable in some special cases. Also, some necessary and sufficient conditions are given for synergic stabilizability problems of a special model by using the traditional Nyquist criterion. The synergic stabilizability problems for the general two-node-network are discussed by using the small gain theorem and matrices decomposition.Then, the Hx control problems for Hadamard synergic control are discussed. The corresponding sufficient conditions are given by using Linear Matrix Inequalities (LMIs) method.Furthermore, some practical applications of the Hadamard synergic control are investi-gated based the above discussions. The problem of a kind of synergic control among a col-lection of vehicles using intervehicle communication and internal output feedback in which the weights of the corresponding edges are considered as the control variables is studied. The general description of this new kind of synergic control is presented via the of the infor-mation flow.Finally,the applications of the Hadamard synergic control method in the SARS epi- demies control are investigated for both single zone and multi-zone. The conditions for disease prevalence are given. It is shown thatζ./, the levels of hygiene precautions during isolation, is a critically important parameter for controlling SARS outbreaks. The influence of the population mobility among zones for SARS control is considered. The relationships among the disease prevalence and mobile population as well as the number of the zone are presented.