Robust Dissipative Control For A Class Of Uncertain Singular Nonlinear System

In early 1970s, Rosenbrock first introduced the model of singular systems when he was reading up on the complex electric network system, from then, overwhelming enthusiasm has been poured into the study of singular system, and consequently a large number of research findings have been acquired. However, these results tend to be for certain systems only. In other words, they are under the assumption that systems possess certain results and known parameters. Yet in practical systems, some uncertain parameters would emerge on account of all forms of unavoidable factors. Therefore, the results related to uncertain singular systems deserve more interests and attention of specialists.The implication of dissipative theory is that the energy consumption of a system is always less than the supply rate of the energy. The dissipativeness contains small gain and passivity as special cases. On the premise of system stability, H∞control aims to design a controller such that L2 gain of the mapping from the disturbances to output is less than or equal to a prescribed level. The passivity, which takes the product of the input and output as the supply rate of energy, has been widely applied in many engineering fields, such as circuits and thermodynamic systems.The paper discusses the robust dissipative problem for a class of nonlinear singular uncertain systems with nonlinear disturbances. Meanwhile, the paper also focuses on the problem of robust dissipative control for nonlinear singular systems which are subjected to dissipative uncertainty. The main content of this paper is summarized as followed:(1) The main background of the problem discussed in this dissertation is introduced. Firstly, the structure characteristics and application background for singular systems are introduced. Then the development and recent progress are presented for singular systems. Furthermore, the significance and recent development of dissipative control and passive control problem for both normal and singular systems are reviewed. Meanwhile, some relevant knowledge of both robust control theory and LMI is introduced. Finally, the main work of this dissertation is listed. (2) Some basic knowledge of dissipative theory is introduced, including definitions of permission and dissipativeness for singular systems, together with common math tools. The definitions both frequently used and cited in this paper are emphasized, for most of the work in this thesis is on the basis of these definitions.(3) We present one of our main results on the robust dissipative control, consider the robust dissipative problem for a class of nonlinear singular systems under nonlinear perturbation. Nonlinear state feedback, nonlinear derivative feedback as well as nonlinear output feedback controller are designed to guarantee the robust dissipativeness of the closed-loop system. Furthermore, we show that the closed-loop system with the designed controller is asymptotically stable for all admissible uncertainties. Finally, numerical example is presented to show the effectiveness of the proposed methods.(4) We consider a class of uncertain nonlinear singular systems with dissipative uncertainty, which contains norm-bounded uncertainty, positive real uncertainty and uncertainty satisfying integral quadratic constraints (IQCs) as special cases. More precisely, we are concerned with the design of a state feedback nonlinear controller such that the closed-loop system is robust dissipative for all admissible uncertainties. This problem contains both robust H∞control and passivity control as special cases. Finally, the closed-loop system with the designed controller is also asymptotically stable if some additional condition on the dissipative uncertainty is imposed.(5) A summary of this paper is given. At the same time, we give an expectation for the future work.