Research On Synthetic Control Problems Of Nonlinear Singular Systems

Since 1970, many scholars in the world have been attracted to the research on theory and application of singular systems. Now, a great progress has been made. With the development of the research, it is found that many practical systems, such as economic systems, robot systems, constrained mechanical systems, power systems and so on, belong to singular systems, so that, singular systems are a class of important systems in engineering applications, and have attracted a lot of attention in recent years. Nearly complete theoretical framework has been established for linear time-invariant singular systems. Compared with the research on linear singular systems, however, the development of nonlinear singular systems is so slow that the results of fundamental theory are very few. Especially, the geometric theory of nonlinear systems has hardly been applied to nonlinear singular systems.The methods used in this dissertation include matrix, algebra as well as differential geometry theory. Relative degree and decoupling of nonlinear singular systems, input-output decoupling and asymptotic output tracking of nonlinear singular control systems are discussed. The main contributions are as follows:1. The concept of relative degree of nonlinear singular systems is introduced. The relation between the relative degree of original nonlinear singular systems and that of the systems via feedback control law are discussed. A coordinate change is introduced such that the control system can be expressed in a simple form. By means of the simple form, the feedback control law is constructed in which the control system can be realized input-output decoupling.2. Input-output decoupling of nonlinear singular systems without the relative degree is considered. The new decoupling algorithm is developed, and the coordinate transformation is introduced via this algorithm such as the systems assumes a set of simple form, and the feedback control law in which the closed-loop system can realize input-output decoupling is also constructed.3. Appling decoupling algorithm to asymptotic output tracking of nonlinear singular control systems. The coordinates transformation is constructed via the decoupling algorithm and a generalized normal form is obtained by using this coordinates transformation. Asymptotic output tracking of nonlinear singular control systems is discussed via this generalized normal form. The feedback law in which the systems can be realized asymptotic output tracking is obtained.