Output-Feedback Control Analysis And Design For Several Classes Of Uncertain Nonlinear Systems

Feedback control of nonlinear systems is a central problem in control science, which is widely used in industry, national defense and other aspects of real life. For example, antiswing positioning control of underactuated cranes, robot motion control, robust attitude tracking control system of spacecraft. In recent decades, with the rapid development of science and technology, strong nonlinearities and serious uncertainties exist in the practical systems, and hence, it is important to search effective control design methods to achieve the desired control objectives for the uncertain nonlinear systems, which has attracted persistent attentions.In the uncertain nonlinear systems, though the strong nonlinearities and se-rious uncertainties would make the nonlinear systems become more general, it also can bring essential difficulties in the analysis and design of nonlinear systems. When only partial system states are available, the control analysis and design of nonlinear systems via output-feedback is very necessary. When the systems allow strong nonlinearities and serious uncertainties, it is more difficult to achieve the control analysis and design of the uncertain nonlinear systems. Based on this, the dissertation studies the global output-feedback control for several classes of uncertain nonlinear systems.By introducing the appropriate dynamic high-gain to deal with the nonlin-earities of the systems and serious unknowns resulting from the systems as well as the reference signal, and the ideas of dead zone and backstepping method are also introduced. The dissertation investigates global adaptive practical track-ing via output-feedback for several classes uncertain nonlinear systems and global output-feedback stabilization for a class of stochastic nonlinear systems. The main contents of this dissertation are composed of the following four parts:(I) Global practical tracking via adaptive output-feedback for un-certain nonlinear systems with function control coefficientsThis part is Chapter 3 of the dissertation, and studies the global practical tracking via adaptive output-feedback for a class of uncertain nonlinear systems with generalized control coefficients. Notably, the system in question has the function-of-output control coefficients and the serious unknowns in the system and the reference signal, and hence is essentially different from the existing closely related literature. To solve the global practical tracking, a high-gain observer is first introduced to reconstruct the unmeasurable system states, and then an adaptive output-feedback controller is designed. It is worth emphasizing that the gains in the designed observer and controller are functions of time and output, for which a novel updating law of the high-gain is introduced to overcome the additional system nonlinearities and the serious unknowns mentioned above. The designed controller is shown such that all the states of the closed-loop system are globally bounded, and furthermore, tracking error will be ultimately prescribed sufficiently small.(II) Further results on global practical tracking via adaptive output-feedback for uncertain nonlinear systemsThis part is Chapter 4 of the dissertation, and considers the global practi-cal tracking via adaptive output-feedback for a class of uncertain nonlinear sys-tems. The system under investigation possesses function control coefficients, the polynomial-of-output growth rate and serious unknowns in the system nonlinear-ities and the reference signal, and hence is essentially different from those in the closely related literature. To solve the problem, a high-gain observer is introduced to reconstruct the unmeasured system states. The involved high-gain is the mul-tiplication of two dynamic gains:one is to compensate the polynomial-of-output in the system growth rate, and the other one is to overcome the serious unknowns in the system and reference signal and the extra system nonlinearities in function control coefficients. Based on the high-gain observer, an adaptive output-feedback controller is successfully designed to guarantee that, for any initial condition of the system, all signals of the closed-loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time.(III) Global practical tracking for nonlinear systems with more un-knowns via adaptive output-feedbackThis part is Chapter 5 of the dissertation, and investigates the global practical tracking via adaptive output-feedback for a class of uncertain nonlinear systems. Essentially different from the closely related literature, the system under investi-gation possesses unknown time-varying control coefficients and a polynomial-of- output growth rate, and meanwhile, the system nonlinearities and the reference signal allow serious unknowns. For this, an adaptive observer is designed to recon-struct the system unmeasured states, where a new dynamic gain is introduced to compensate the serious unknowns in the system nonlinearities and the reference signal. Based on this and by backstepping technique, an adaptive output-feedback controller is successfully designed, such that all the states of the closed-loop sys-tem are bounded, and the tracking error will be prescribed sufficiently small after a finite time.(IV) Global output-feedback stabilization for stochastic nonlinear systems with function control coefficientsThis part is Chapter 6 of the dissertation, and investigates the global output-feedback stabilization for a class of stochastic nonlinear systems with function con-trol coefficients. Notably, the systems in question possess the control coefficients which are functions of output, rather than constants, and hence are essentially different from the existing literature on stochastic stabilization. To solve the con-trol problem, an appropriate reduced-order observer is introduced to reconstruct the unmeasured system states, and then a smooth output-feedback controller is successfully designed by using the backstepping method, which guarantees that the closed-loop system is globally asymptotically stable in probability.The above four parts give the corresponding simulation examples, which il-lustrate the effectiveness and feasibility of the proposed control design schemes, respectively.