Adaptive Control Analysis And Design For Minimum Phase Systems With Unknown Relative Degree And High Frequency Gain

The dissertation mainly focuses on the investigation of high-gain adaptive control for minimum phase SISO (single-input-single-output) linear systems. First, we solve the derivative output feedback high-gain adaptive stabilization for sys-tems with known relative degree. Second, we solve the high-gain adaptive sta-bilization and the zero static error tracking control for systems with unknown relative degree and high frequency gain. The main content of the dissertation consists of the following three parts:(I) Derivative output feedback high-gain adaptive stabilization for minimum phase systems with known relative degreeThis part, the first section of Chapter3of the dissertation, studies the adap-tive stabilization for a class of minimum phase SISO linear systems with known relative degree. By transforming system into Isidori normal form, and analyzing the influence of relative degree to the stable zero dynamic, we design a deriva-tive output feedback high-gain adaptive controller. In terms of the method of Lyapunov stability, we prove that the closed-loop system is asymptotically stable. Different from the existing literature, the design method for the adaptive law of the derivative output feedback high-gain adaptive controller is presented.(II) High-gain adaptive stabilization for minimum phase systems with unknown relative degree and high frequency gainThis part, the second section of Chapter3of the dissertation, studies the adaptive stabilization for a class of minimum phase SISO linear systems with unknown relative degree and high frequency gain. By flexibly choosing the design parameters of the high-gain adaptive controller, the effect on stability caused by the unknown high frequency gain is eliminated. Since the design method only requires that the sign of high frequency gain is known, rather than its value, the restrictions on the system are greatly relaxed. Moreover, we improve the design methods of the adaptive law in the existing literature, and give a more general form of the adaptive law. (Ⅲ) Zero static error tracking control for minimum phase systems with unknown relative degree and high frequency gainThis part, Chapter4of the dissertation, studies the zero static error tracking control for a class of minimum phase SISO linear systems with unknown relative degree and high frequency gain. Different from the existing literature, the studied systems not only have an input disturbance but also have an output disturbance. By applying internal model principle, and cascading the system with the common unstable model of the external signals, we design a controller such that the close-loop system output asymptotically follows the command signal while achieving the disturbance attenuation.For the theoretical results obtained in above three parts, the corresponding simulation examples are present to illustrate the effectiveness and feasibility of the proposed controller design methods.