Robust And Adaptive Designs Of Nonlinear Systems Control

In the vast majority of applications, the essential problem in the design of nonlinear systems is that dynamics of the plant are partially known and can not be precisely known. Using the mathematical model for control system to describe the real plant, there exist unknowns and uncertainties between them. As an interesting research area, control of nonlinear uncertain systems has attracted lots of researchers since 1950's. The uncertainties may degrade the performance of a controlled system or even make the closed-loop system unstable when they are not appropriately accounted for in the controller design stage. To deal with various unknowns and uncertainties, online estimation and robustness are the key in designing a successful controller. Adaptive control, robust control and their combinations represent the effective means to deal with whatever uncertainties and achieve a guaranteed transient performance and final tracking accuracy.According to unknowns and uncertainties shown in different form in plants, the stability analysis and control problem for semi-strict feed back nonlinear systems and nonlinear parameterized nonlinear systems are studied in this dissertation. Based on the nonlinear robust control, adopting the discontinuous projection-based parameter estimator, the designed adaptive robust controllers guarantee that the semi-strict feed back nonlinear systems stable and satisfied the transient performance and final tracking accuracy. To nonlinearly parameterized nonlinear systems, the adaptive control based on immersion and invariance approach is used. Through choosing suitable estimator tunning function (β(·)), which renders the nonlinearly parameterized part monotone, the nonlinearly parameterized nonlinear systems achieve asymptotic stabilization.The main contents of this dissertation are outlined as follows,(1) The discontinuous projection based adaptive robust control approach is extended to a class of nonlinear systems subjected to parametric uncertainties as well as all three types of nonlinear uncertainties - uncertainties could be state-dependent, time-dependent, and/or dynamic. The proposed approach differentiates between dynamic uncertainties with and without known structural information and achieves not only for global stability, but also for a guaranteed robust performance. (2) Nonlinear observers are incorporated into the discontinuous projection based adaptive robust control to synthesize performance oriented controllers for a class of uncertain nonlinear systems with unknown sinusoidal disturbances. In addition to magnitudes and phases, frequencies of the sinusoidal disturbances need not to be known as well, so long as the overall order is known. The adaptive robust control laws effectively deal with various uncertainties for a guaranteed robust performance.(3) A discontinuous projection-based output feedback adaptive robust learning control (OARLC) scheme is constructed for a class of nonlinear systems with general period disturbance signal in a semi-strict feedback form by incorporating an observer. An observer is first designed to provide exponentially convergent estimates of the unmeasurable states. Using certain known basis functions to capture the characteristics of unknown general periodic disturbances, the discontinuous projection type adaptation law can then be used to tune the amplitudes of those basis functions on-line to recover the unknown general periodic disturbances asymptotically. The estimation errors due to the unknown initial states, uncompensated disturbances, and the uncertain nonlinearities are also effectively dealt with via certain robust feedback at each step of the proposed OARLC backstepping design. The resulting controller achieves a guaranteed transient and a prescribed final tracking accuracy for output tracking performance.(4) A new framework to design adaptive controllers for nonlinearly parameterized systems is proposed. The key step is the construction of a monotone function, which effectively becoming a synthesis tool. One consequence of this fact is that the controller does not rely on state-dependent switching. In order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced Immersion and Invariance (I&I ) approach.Finally, the adaptive robust controller for semi-strict feedback nonlinear systems is outlined and the perspective of the future studies is referred. On the other hand, the adaptive control for nonlinearly parameterized systems is outlined also and future work for such systems is also pointed out at the end of the dissertation.