The Research On Adaptive Backstepping Fuzzy Control For Several Classes Of Nonlinear Systems

In recent years, many new control theories have been gradually established because ofthe controlled plants and the control objectives becoming more and more complex. For thecontrol problem of the complex nonlinear systems, the much more effective control methodis the fuzzy control technology. Moreover, the applications of the fuzzy control theory in theactual production and daily life has been concerned with its development. In the existing fuzzycontrol theory, the fuzzy logic systems(FLS) control method receives more and more attentionfrom the scholars. The main advantage of the method is that it can combine some experienceand knowledge from designers or experts to investigate the stability and the controller designproblem of the nonlinear systems. However, the main disadvantage of the method is that due tothe characteristic of the FLS such that there is no systematic stability theory analysis method,and this also is the challenging of the use of the FLS control method. On the other hand, duringthe controller design process, the number of the adjusted parameters depends on the number ofthe fuzzy rule bases. With an increase of fuzzy rules, the number of parameters to be estimatedwill increase significantly, therefore, for the actual industrial systems, during the controllerdesign process, it is extremely necessary to design the controller containing much less adjustedparameters. In addition, in the practical systems, the time delay is one of the main factorswhich make the system unstable. In this dissertation, the effective adaptive fuzzy controllersare proposed for the nonlinear systems with discrete or distributed time-varying delays. And inorder to reduce the online computation burden of the systems, the proposed controllers containmuch less adjusted parameters. Specifically, we obtain the following research results.1. Based on the reasonable assumptions, by utilizing the appropriate Lyapunov-Krasovskiifunctional, the FLS and the Nussbaum-type functions to deal with the unknown time-varyingdelay terms, approximate the unknown nonlinear continuous functions and detect the controldirections of the systems, respectively, finally, for the nonlinear systems with discrete timedelays and unknown control directions and the nonlinear systems with distributed time delaysand unknown control directions, the adaptive fuzzy tracking controllers are designed by usingthe backstepping technique. Moreover, the proposed controllers contain much less adjustedparameters such that the use of the controllers are much more convenient and effective.2. Based on the reasonable assumptions and the linear state observer, for the time-varyingdelay nonlinear systems with unknown control directions and the nonlinear systems with inputdelay, the output feedback adaptive fuzzy controllers are proposed by combining the properLyapunov-Krasovskii functional, the Nussbaum-type functions, the minimal learning parame-ters (MLP) algorithm, the FLS and the backstepping technique. It is should be pointed out thatbefore the controllers are designed, we introduce a linear state transformation, through which the unknown control coefficients distributed in the system can be lumped together, then, theproblem is become that how to design the output feedback controllers for the relatively com-mon systems with only one unknown direction, and it is worth noting that the controllers containmuch less adjusted parameters.3. For the nonlinear time-varying delay systems with unknown dead zone and the MIMOnonlinear system with input delays, the adaptive fuzzy controllers which contain much lessadjusted parameters are constructed by combining the proper Lyapunov-Krasovskii functional,the dynamic surface control (DSC) technique, the MLP algorithm, the FLS and the backsteppingtechnique. It is should be pointed out that the use of the DSC technique effectively overcomethe“explosion of complexity” cased by the use of the backstepping technique, therefore, thecontroller design process is simplified effectively. Moreover, the controllers contain very fewadaptive parameters (one or two) such that the online computation burden is reduced greatly.4. Most of the existing results investigating the tracking control problem of the stochasticnonlinear systems are obtained by using the quartic Lyapunov functions or by combining theclassical quadratic functions with the risk-sensitive cost criterion. However, in this dissertation,the hyperbolic tangent functions are introduced to deal with the Hessian terms which comefrom the Ito differential, and then, by applying the classical quadratic functions, the backstep-ping technique and the FLS, the effective fuzzy adaptive tracking controller is designed for thestochastic nonlinear time-varying delay system.