Approximators-Based New Methods Of Adaptive Control

During the last two decades, uncertain nonlinear systems control has always been one of the focuses in automatic control community. Especially, approximators-based adaptive control has attracted much attention of many researchers and some important results have been obtained. However, there still exist some open issues need to be further investigated.This dissertation is devoted to solve the global stability and given tracking accuracy control problems left unsolved in previous work. For several classes of uncertain nonlinear systems,two new methods of approximators-based adaptive control are proposed. Details are listed as follows:1. In Chapter 3, for a class of uncertain nonlinear systems in strict-feedback form, the globally stable adaptive neural network tracking control problem is investigated. By using radial basis function(RBF) neural networks to compensate for system uncertainties in each backstepping design procedure, a novel adaptive neural network controller is developed based on the constructed smooth switching function. Under the obtained controller, the global uniform ultimate boundness of all the closed-loop signals is guaranteed, and the output of the system converges to a small neighborhood of the reference trajectory by properly choosing the design parameters. The main feature of the proposed controller lies in that it includes two parts: a traditional adaptive neural control law that dominates the approximation active domain and an extra robust control law that takes charge outside the approximation domain.This construction of the controller will be used repeatedly in the following chapters to design the desired controllers.2. In Chapter 4, based on the results obtained in Chapter 3, we address the globally stable control problem with a priori known tracking accuracy for a class of uncertain strict-feedback systems. To solve this problem, two new nth-order continuously differentiable switching functions are constructed to develop control law, and Barbalat lemma is introduced to analyze the convergence of the tracking error. By combining adaptive fuzzy control with the backstepping technique, a multiswitching-based robust adaptive fuzzy controller is designed. It has been proved that the controller guarantees that all the closed-loop signals are globally uniformly ultimately bounded and the tracking error converges to an accuracy that is assigned a priori.3. In Chapter 5, the control schemes proposed in Chapters 3 and 4 are extended to a class of uncertain nonlinear multi-input/multi-output(MIMO) systems in block-triangular form. Firstly, a semi-globally stable adaptive neural network control scheme is developed to guarantee that the ultimate tracking errors satisfy the accuracy known a priori. Then, under the system functions with some bounding restrictions, we improve previous control method such that the tracking errors converge to the given accuracy, as well as the closed-loop system is globally stable.4. In Chapter 6, we study the extension of the control strategy proposed in Chapter 4to uncertain nonlinear time-delay systems. For a class of nonlinear strict-feedback systems with unknown disturbances and time delay, under some assumptions, a multiswitching-based adaptive backstepping neural network state-feedback controller is designed via the constructed nonnegative functionals. It has been proved that the proposed controller guarantees the global uniform ultimate boundness of all the closed-loop signals, and the system output converges to a priori known accuracy.