Approximate Design Of The Optimal Output Tracking Control Law For Nonlinear Time-Delay Systems

The optimal output tracking (OOT) problem is one of the important application areas of the optimal control (OC) theory. The theory of OOT has made a development with the formulation and development of the OC theory at the end of 1950s and the start of 1960s. In recent years, Modern industries and national defenses have achieved great advancement, which results in more and more applications of the theory of OOT in the ocean information detection technique, space technique, economic systems, intelligent robot, and chemical industry and so on. Moreover, there are few results on the OOT problem of nonlinear time-delay systems. The reason generally arises from its double complexity. Therefore, the analysis of OOT problem for nonlinear time-delay systems is a significant research both in theory and in practice.Firstly, the relative studies on the OOT problem for nonlinear time-delay systems up to now are given in detail. Then, based on the maximum principle, this dissertation considers the OOT problem for a class of nonlinear, time-delay systems whose reference input to be tracked is produced by a general exosystem. The existence and uniqueness of the OOT control law are studied and an approximate design processdure of the law is given. The physical realization problem of the feedforward control is discussed. The main contents are given as follows.1. Some problems relative to OOT are presented with their main research methods at first. Then, a detail expression of studies is introduced on the OOT problem for bilinear systems, nonlinear systems, nonlinear systems with the time-delay in the state, and nonlinear time-delay systems under external disturbances. The objective and contents of this dissertation are given finally.2. The OOT problem for a class of bilinear systems with a quadratic index performance is studied. The bilinear term described by a product of the state vector and the control vector in the systems'equation is considered as the perturbation of systems. By introducing an adjoint vector, the nonlinear two-point boundary value (TPBV) problem derived form the necessary condition of the maximum principle is replaced by a new TPBV problem which is described by a state equation and an...