Global Robust Stabilization and Output Regulation of a Class of Nonlinear Systems with Unknown High-Frequency Gain Sign

The output regulation problem is a central problem in control theory. The early work on output regulation problem in the state space framework can be traced to the early 1970s, and the problem of nonlinear systems has been an active topic since 1980s. So far there exist various results of this problem under various assumptions. In the case where the high-frequency gain sign is unknown, the global robust output regulation problem of nonlinear systems with nonlinearly parameterized uncertainties has not been considered. The sign of the high-frequency gain is also called the control coefficient and its sign determines the control direction, with which the control design becomes much more tractable. However, the knowledge of it may not always be available. In this thesis, we will study the global robust stabilization problem and the global robust output regulation problem of a class of nonlinear systems with unknown high-frequency gain sign, and the solvability of the first problem will lay a foundation of that of the second one. The thesis consists of two parts. In the first part, the global robust stabilization problem for nonlinear systems in output feedback form is addressed. An output feedback adaptive control scheme is developed to solve the problem by integrating the robust control method and the adaptive control method. In the second part, the global robust output regulation problem for nonlinear systems in output feedback form with unknown high-frequency gain sign is handled by further developing the idea in the first part. This part can be treated as an extension of the previous one. The contribution of this thesis is that, by integrating the robust control approach and the adaptive control approach, we have overcome the dilemma caused by the nonlinearly parameterized uncertainties and the unknown high-frequency gain sign, and have established a feedback adaptive control scheme to handle the proposed two problems. Also, the derivation of the method gives an alternative solution to the global robust output regulation problem when the high-frequency gain sign is known, which has been addressed by the small gain theorem in the existing literatures.