Adaptive Practical Output Tracking Control For High-order Uncertain Nonlinear Systems

The control design problems for high-order nonlinear systems have been widely studied by researchers in the last few years. Such systems represent the more general forms of the strict-feedback nonlinear systems, whose Jacobian lin-earization may have uncontrollable or unstable modes at the origin. Therefore, how to solve the control problems of the high-order nonlinear system is more dif-ficult than those of the strict-feedback nonlinear systems. In addition, the high-order nonlinear systems contain a class of underactuated, weakly coupled, unstable mechanical systems which are comprehensively used in the helicopters, spacecraft, robots, surface vessels and underwater vehicles. Therefore, the investigation for the high-order nonlinear systems is of theoretical and practical importance.Based on the adding a power integrator, this thesis investigates the smooth adaptive practical output tracking control for the high-order uncertain nonlinear systems. First, we summarize the tracking control theory of the high-order un-certain nonlinear systems, including the subject background, the theoretical and practical importance and the research status. Then we introduce the basic idea of adding a power integrator by a simple example and summarize the procedure of this method. Finally, we solve the following tracking control problems for two classes of high-order uncertain nonlinear systems:(Ⅰ) Practical output tracking control for a class of high-order un-certain nonlinear systems with a known reference signalIn this part, the problem of practical output tracking control is investigated for a class of high-order uncertain nonlinear systems with a known reference signal, unknown control coefficients and zero dynamics. Different from the existing liter-atures, the high-order uncertain nonlinear systems studied here are more general: (1) the systems have the zero-dynamics which are unmeasured; (2) The control coefficients are unknown, and the low bounds of the control coefficients consist of unknown constants and known functions. By state-feedback, skillfully using the adding a power integrator, the adaptive technique and some inequalities, we give the design procedure of the smooth adaptive practical output tracking controller. The constructed state-feedback tracking controller guarantees that all states of the closed-loop systems are globally bounded, and the tracking error can be bounded by any given positive number after a finite time. Finally, a simulation example is given to illustrate the correctness of the theoretical results.(Ⅱ) The practical output tracking control for a class of high-order uncertain nonlinear systems with an unknown reference signalIn this part, the problem of practical output tracking control is studied for a class of high-order uncertain nonlinear systems while the reference signal is unknown. Based on the idea of the above problem, by using inequations skillfully and appropriate disposal for the unknown control coefficients and nonlinear terms, we overcome the difficult brought by the unknown reference signal, and design the practical output tracking controller. Then, by some theories such as Lyapunov theory and Barbalat lemma, we prove that the states of the closed-loop systems are globally bounded, and the tracking error can be bounded by any given positive number after a finite time. Finally, a simulation example is given to illustrate the correctness and the validity of the theoretical results.