Output Regulation With Nonlinear Exosystem And Its Application To Attitude Control Of Spacecraft

The problem of output regulation is one of the most important issues in the controltheory. The objective of the output regulation is to design a feedback controller for an un-certain system such that the closed-loop system is stable, and the output of the closed-loopsystem can asymptotically track a class of desired trajectories in the presence of a classof disturbances. Therefore, the output regulation problem includes the stabilization, theasymptotic tracking of desired trajectories and asymptotic disturbance rejection as specialcases. Since the dynamic equations of a spacecraft are nonlinear and strongly coupled, andthe attitude control problem of a spacecraft often involves a series of problems, such asattitude stabilization, attitude tracking and disturbance rejection. The output regulationtheory could be a proper tool to solve the attitude control problem of a spacecraft. Mostexisting works on nonlinear output regulation problem rely on the assumption that theexosystem is linear, which severely restricts the development of output regulation theoryand applications. Therefore, it has important theory and practice significance to general-ize the output regulation theory, and then apply the new theoretical results to the problemof attitude control and disturbance rejection of the spacecraft. The main contributions ofthis dissertation are the following:1. The problem of global robust output regulation for a class of uncertain nonlinearsystems with nonlinear exosystems and unknown control direction is investigated. With-out the knowledge of the control direction, and under the presence of nonlinear exosys-tem, a dynamic output feedback control law is designed to solve the corresponding globalrobust output regulation problem by combining the techniques from Nussbaum dynamicgain, nonlinear internal model and robust stabilization.2. Global robust output regulation problem for a class of minimum phase uncertainnonlinear systems with nonlinear exosystem is addressed. Under the assumption that thesolution to the regulator equation of the nonlinear system satisfies a class of nonlinearequations, the previous assumption that the exosystem must have the form of finite Taylorexpansion can be removed; a nonlinear internal model design method is proposed, whichis independent of the exogenous signal. Based on the proposed internal model, an outputfeedback control law is presented using the Lyapunov method. 3. Global robust output regulation problem for a class of non-minimum phase non-linear systems with nonlinear exosystem is considered. A nonlinear internal model isdesigned using the immersion system technique. The minimum phase constraint condi-tion of the nonlinear system is removed using the changing supply function technique,and under the assumption that part of the solution to the regulator equations is a constant,which is independent of the exogenous signal and uncertain parameters. By combining thechanging supply function technique and dynamic gain technique, a state feedback controllaw is given.4. The problem of attitude tracking and disturbance rejection are studied for rigidspacecraft by using the nonlinear internal model. It is the first time that the uncertain-ty in the inertia matrix is handled by combining the methods from semi-tensor productof matrices and adaptive control, the advantage in respect of control performance of theproposed method is also revealed through simulation results. A dynamic compensator de-pending on the exogenous signal is presented when the inertia matrix is uncertain, and asemi-tensor product based adaptive attitude tracking and disturbance rejection controlleris given, based on the proposed dynamic compensator. Furthermore, a dynamic compen-sator free from the exogenous signal is provided when the inertia matrix is known, anda control law for attitude tracking and disturbance rejection of spacecraft is shown usingLyapunov method.