Adaptive Control Algorithm Design For Several Classes Of Nonlinear Discrete-time Systems

Currently, the study of the nonlinear discrete systems for intelligent control algorithm is the hotspot of the research for nonlinear control theory. In this paper, in order to deal with the nonlinear discrete systems in different form, a class of Neural network-based algorithm is introduced to design the suitable controller and appropriate adaptive laws, and the propose of the control algorithm can be achieved based on Lyapunov stability theorem. This thesis is studied through the following three aspects:(1) An adaptive neural network control algorithm is given for a class of multi-input multi-output nonlinear discrete systems in strict form with uncertain. Because of the complexity of system structure, the controller design and stability analysis of the system is more difficult than the past. To stabilize these systems, a new recursive procedure is developed and the effect caused by the noncausal problem in nonstrict feedback discrete-time structure can be solved by using a semirecurrent neural approximation. Based on the difference Lyapunov approach, it is proved that all the signals of the closed-loop system are semi-global ultimately uniformly bounded and a good tracking performance can be guaranteed, finally. The feasibility of the proposed controllers can be validated by setting two simulation examples.(2) An adaptive neural network tracking control is studied for a class of uncertain nonlinear discrete-time systems with unknown time-delay. Firstly, based on the Lipschitz condition, the norm-boundedness assumption of the unknown nonlinearities and the Mean-value theorem, the unknown time-delay problem is solved. In order to overcome the noncausal problem, the strict- feedback systems are transformed into a special form. The radial basis functions neural networks(RBFNNs) are utilized to approximate the unknown functions of the systems, the adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov stability analysis theory, it is proven that the closed-loop system is stable in the sense that semi-globally uniformly ultimately bounded(SGUUB) and the output tracking errors converge to a bounded compact set. A simulation example is used to illustrate the effectiveness of the proposed algorithm.(3) An adaptive predictive control algorithm is employed to control a class of continuous stirred tank reactor(CSTR) system in discrete-time form and the none-symmetric dead-zone inputs are considered here. The design parameters of the control algorithm for the CSTR systems are not so much than before, such that the calculated amount of the control algorithm is less than before. The unknown functions are approximated by the radial basis function neural networks(RBFNN), and the mean value theorem is utilized to resolve the implicit function, then the suitable controller and the reasonable adaptive laws are constructed. Based on the Lyapunov analysis method, and choosing the design parameters appropriately, all the signals in the closed-loop system are proved to be semi-global uniformly ultimately bounded(SGUUB) and the tracking error is converged to a small compact set. A simulation example for CSTR systems is studied to demonstrate the effectiveness of the proposed approach.