Interconnection Control Of Dynamic Systems

It is good for us to study the modeling and control of dynamic systems in behavioral framework in which no unnecessary structure is assumed of systems. The central object of study on systems is its behavior. Under behavioral approach, the limitation exists in traditional paradigm was broken through. This approach provides us a more natural way to do research particularly to study of control. The viewpoint of viewing control as interconnection overcomes the deficiencies that exit in the classical feedback control theory. Furthermore, the systems that have different representations can be studied in a uniform way. For these advantages, the task of finding a solution to the problem of control for dynamic systems in behavioral framework have significance in both theory and practice and is a very challenging problem as well.In this paper, the emphasis is that some different kinds of desired behaviors are considered from the perspective of interconnection. Firstly, background of the development of behavioral theory and the history and current situations of it are introduced. The idea of control as interconnection is also presented. Secondly, the basic theory of linear differential systems is given which is the backbone of behavioral theory. Follow it, as the representative paradigm of interconnected systems in classical System Theory, composite systems is studied about modeling and the main properties. From the process we can see the advantages of the behavioral approach. Subsequently, the problems of the pole placement and the construction of observer-based controller are particularly investigated and then the relations are carried out between the interconnected control and classical feedback control in terms of the pole placement problem. Finally, the problem about linear quadratic control is discussed for linear, time-invariant and continuous-time systems. Assuming that the cost function is expressed by means of a quadratic differential form and giving the initial condition, the asymptotically stable optimal behavior is finally achieved. Some examples are provided to show that the present statement within the behavioral setting is a natural extension of the classical linear quadratic problem for state-space models.