Adaptive Fuzzy Optimal Control For A Class Of Nonlinear Discrete-Time Systems With Uncertainties And Its Applications

Optimal control is the hotspot and difficult issue in the field of nonlinear control theoryat present. In this thesis, the adaptive fuzzy control methods which can not only be moreeffective for dealing with the uncertainties of the systems, but also improve the controlperformance of the systems can be proposed for nonlinear discrete-time systems. By using theoptimal control method and introducing the performance index function, the control cost canbe minimized and the optimal control can be achieved. This thesis mainly studies thefollowing three contents:(1) An adaptive fuzzy optimal control approach is constructed for a class of nonlineardiscrete-time systems which contain unknown functions and non-symmetric dead-zone. Thefuzzy logic systems are employed to approximate the unknown functions in the systems.Based on the reinforcement learning algorithm and backstepping technique, the controller isdesigned to make the performance function reach a minimal value then achieve the optimalcontrol. The adaptation auxiliary signal is established to solve the effect of the dead-zone andthe updating laws are obtained based on the gradient rule. Finally, according to the Lyapunovstability theory, all the signals of the closed-loop system are proved to be bounded.Simulation example verifies the feasibility of the proposed control algorithm.(2) Based on the direct heuristic dynamic programming method, the optimal trackingcontrol problem for the Henon Mapping chaotic system can be solved. The fuzzy logicsystems are used to approximate the utility function, and compared with the results the cost ofthe controller is reduced. Finally, the Lyapunov function approach is utilized to analysis thestability of the system, and the tracking error, the adaptation law and the control input can beproved bounded. Simulation results demonstrate the effectiveness of the designed method.(3) An adaptive tracking control issue is studied for the sixth-order induction motormodel which is in discrete-time form. In the design process, make full use of theapproximation properties, and the proposed adaptive approach needs only less designparameters which is different from the existing results, therefore, it can reduce the calculationamount. Under the Lyapunov approach, all the signals of the controlled system can beguaranteed to semi-global uniformly ultimately bounded, and the tracking error can beensured to a small neighborhood around zero. Simulation results show the practicality of thepresented scheme.