Study On Stable Adaptive Fuzzy Control With Actuator Nonlinearity

In recent years, adaptive control for uncertain systems with actuator nonlinearityusing fuzzy systems has been a hot topic in the field of intelligent control. Somecorrelative problems in this area are studied in this paper.Firstly, using Implicit Function Theorem and the Talor series expansion, the form ofthe non-affine nonlinear systems is transformed to the form of affine nonlinear systems.Based on the principle of variable structure control, an adaptive fuzzy control strategywith supervisory controller is designed for the transformed nonlinear system. With thehelp of a supervisory controller, the reSulting closed-loop system is globally stable inthe sense that all signals involved are uniformly bounded. Furthermore, the adaptivecompensation term of the optimal approximation errors is adopted to reduce the effectsof modeling error. By theoretical analysis, it is shown that tracking errors converges tozero.Secondly, based on the principle of variable structure control and the capability ofthe fuzzy systems with linear adjustable parameters, an adaptive fuzzy control strategywith supervisory controller for a class of uncertain nonlinear systems with unknownbacklash-like hystersis is developed. With the help of a supervisory controller, theresulting closed-loop system is globally stable in the sense that all signals involved areuniformly bounded. Furthermore, the adaptive compensation term of the optimalapproximation error is adopted to reduce the effects of modeling error. By theoreticalanalysis, it is shown that tracking error converges to a small neighborhood of zero. Next, the above result is extended to the MIMO interconnected nonlinear systems withunknown backlash-like hysteresis, a decentralized adaptive fuzzy control strategy isdeveloped. The plant dynamic uncertainty and modeling errors are adaptivelycompensated by adjusted the parameters and gains on-line for each subsystems usingonly local information. By theoretical analysis, it is shown that the closed-loop fuzzycontrol systems are globally stable, with tracking error converging to a neighborhood ofzero.Thirdly, two design schemes are proposed for two class of systems with unknowndead-zone, which their structures are different, respectively. Begin with, based on theapproximation capability of fuzzy systems and backstepping technique, and byintroducing modified integral-Lyapunov function, and by utilizing the simplified deadzone model and the property of Nussbaum function, a design scheme of adaptive fuzzycontroller for a class of nonlinear time-varying time-delayed systems with unknownfunction control gain, is proposed. The approach does not require a priori knowledge ofthe sign of the control gain and removes the conditions that dead-zone modelparameters are known constants. In addition, the adaptive compensation term of theapproximation error is adopted to minify the influence of modeling errors and parameterestimation errors. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly, ultimately bounded. Then, the problem of adaptive fuzzycontrol for a class of MIMO time-delayed nonlinear systems with unknown dead-zoneis discussed, and a design scheme of adaptive fuzzy controller with a supervisorycontroller is proposed. By theoretical analysis the resulting closed-loop system, isglobally uniformly ultimately bounded with tracking errors converging to zero.Fourthly, different design schemes for a class of linear or nonlinear systems areproposed, respectively. First, based on the principle of sliding mode control, using thesimplified nonlinear dead-zone model and the fuzzy systems with linear adjustableparameters which are used to approximate plant unknown functions, a design scheme ofadaptive fuzzy controller for a class of SISO nonlinear systems is proposed. Theapproach removes the conditions that the dead-zone slopes and. boundaries are equal, symmetry, respectively. In addition, it does not require the assumptions that allnonlinear dead-zone model parameters are known constants. The adaptive compensationterm of the approximation errors is adopted to minify the influence of modeling errorsand parameter estimation errors. By theoretical analysis, the closed-loop control systemis proved to be semi-globally uniformly ultimately bounded with tracking errorsconverging to zero. Then, the problem of adaptive fuzzy control for a class oflarge-scale time-delayed systems with unknown nonlinear dead-zone is discussed, and adesign scheme of adaptive fuzzy controller is proposed. Lastly, the concept of parralldistributed compensation(PDC) is employed to design the state feedback controller for aclass of uncertain time-delayed systems with input delay and unknown nonlineardead-zone. Based on LMI, by constructing appropriate Lyapunov-Krasovskiifunctional(LKF), sufficient conditions for the existence of fuzzy state feedback gain arederived. By theoretical analysis, the closed-loop control system is proved to be globallyasymptotically stableFinally, the chaos tracking control problem is studied for a class of uncertaintime-delayed chaotic systems with dead-zone and saturating input. Based on theprinciple of sliding mode control (SMC), a novel adaptive design scheme is proposed.The approach not only overcomes the drawback in the existing literature, but alsoremoves the assumptions that the dead-zone is symmetric and the slopes are known. Bytheoretical analysis, it is shown that tracking error asymptotically converges to zero.Through the research in this paper, some fuzzy, control problems for uncertainnonlinear systems with actuator nonlinearity have been properly solved. Numericalsimulation experiments of these Control schemes demonstrate their effectiveness.