Adaptive Fuzzy Control For Several Classes Of Uncertain Nonlinear Systems

This thesis investigates the problem of stabilization and control design for several classes of uncertain nonlinear systems by using backstepping design technique and adaptive fuzzy control theory. The main researches of the thesis are as following:(1) An adaptive fuzzy output feedback control approach is studied for a class of uncertain nonlinear systems with unmeasured states and unknown control directions. In the control design, by using fuzzy logic systems to approximate the unknown nonlinear functions, a nonlinear fuzzy states observer is designed for estimating the unmeasured states. Based on a Nussbaum gain function and adaptive fuzzy backstepping DSC design technique, an adaptive fuzzy output feedback control method is constructed. Meanwhile, the problems of unknown control directions and “explosion of complexity” are solved. It is proved that the proposed control approach can guarantee the semi-globally uniform ultimate boundedness for all the signals of closed-loop system and the tracking errors to a small neighborhood of the origin. Simulation study verified the effectiveness and reasonableness of the proposed approach.(2) An adaptive fuzzy output feedback control approach is proposed for a class of stochastic nonlinear systems with unknown dead-zones and unknown control directions. In the design, by using a linear state transformation, the unknown control coefficient and the unknown slope characteristic of the dead-zone are lumped together, and the original system is transformed to a new system. Fuzzy logic systems are employed to identify the uncertain nonlinear systems, a nonlinear fuzzy states observer is constructed to solve the problem of unmeasured states. Based on a Nussbaum gain function and adaptive fuzzy backstepping DSC design technique, a new adaptive fuzzy output-feedback controller is constructed. And it solves the problems of unknown control directions and “explosion of complexity”. The stability analysis proves that all the variables of closed-loop system are bounded in probability and tracking error converges to a small neighborhood of zero by Lyapunov function theorem. A numerical example is studied to verify the effectiveness and rationality of the proposed control method.(3) The composite adaptive fuzzy output feedback control problem is investigated for a class of stochastic nonlinear systems, where the input signal takes quantized values. In the control design, by using fuzzy logic systems to modeling for controlled systems, a nonlinear fuzzy states observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy states observer, a serial-parallel estimation model is established. Based on adaptive fuzzy backstepping DSC technique and the prediction error between the system states observer model and the serial–parallel estimation model, an adaptive output feedback controller with the composite parameters adaptive laws is constructed. The stability analysis is proposed to prove that all the variables of closed-loop system are bounded in probability and tracking error converges to a small neighborhood of zero by Lyapunov function theorem. Mumerical and actual examples are studied to verify the effectiveness and practicability of the proposed approach.(4) The composite adaptive fuzzy output feedback decentralized control approach is proposed for a class of nonlinear stochastic large-scale systems with unknown dead-zones and unmeasured states. In the design, with the help of fuzzy logic systems to identify the unknown nonlinear functions, a nonlinear fuzzy states observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy states observer, a serial-parallel estimation model is established. Based on adaptive fuzzy backstepping DSC technique, decentralized control theory and the prediction error between the system states observer model and the serial-parallel estimation model, a composite adaptive fuzzy decentralized controller is constructed. The designed controller with the composite parameters adaptive laws ensures that all the variables of closed-loop system are bounded in probability and tracking errors converge to a small neighborhood of zero based on Lyapunov function theorem. A numerical example is studied to verify the effectiveness and rationality of the proposed approach.