Design of stable adaptive fuzzy control.

by John Tak Kuen Koo.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 217-[220]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- "Robust, Adaptive and Fuzzy Control" --- p.2Chapter 1.3 --- Adaptive Fuzzy Control --- p.4Chapter 1.4 --- Object of Study --- p.10Chapter 1.5 --- Scope of the Thesis --- p.13Chapter 2 --- Background on Adaptive Control and Fuzzy Logic Control --- p.17Chapter 2.1 --- Adaptive control --- p.17Chapter 2.1.1 --- Model reference adaptive systems --- p.20Chapter 2.1.2 --- MIT Rule --- p.23Chapter 2.1.3 --- Model Reference Adaptive Control (MRAC) --- p.24Chapter 2.2 --- Fuzzy Logic Control --- p.33Chapter 2.2.1 --- Fuzzy sets and logic --- p.33Chapter 2.2.2 --- Fuzzy Relation --- p.40Chapter 2.2.3 --- Inference Mechanisms --- p.43Chapter 2.2.4 --- Defuzzification --- p.49Chapter 3 --- Explicit Form of a Class of Fuzzy Logic Controllers --- p.51Chapter 3.1 --- Introduction --- p.51Chapter 3.2 --- Construction of a class of fuzzy controller --- p.53Chapter 3.3 --- Explicit form of the fuzzy controller --- p.57Chapter 3.4 --- Design criteria on the fuzzy controller --- p.65Chapter 3.5 --- B-Spline fuzzy controller --- p.68Chapter 4 --- Model Reference Adaptive Fuzzy Control (MRAFC) --- p.73Chapter 4.1 --- Introduction --- p.73Chapter 4.2 --- "Fuzzy Controller, Plant and Reference Model" --- p.75Chapter 4.3 --- Derivation of the MRAFC adaptive laws --- p.79Chapter 4.4 --- "Extension to the Multi-Input, Multi-Output Case" --- p.84Chapter 4.5 --- Simulation --- p.90Chapter 5 --- MRAFC on a Class of Nonlinear Systems: Type I --- p.97Chapter 5.1 --- Introduction --- p.98Chapter 5.2 --- Choice of Controller --- p.99Chapter 5.3 --- Derivation of the MRAFC adaptive laws --- p.102Chapter 5.4 --- Example: Stabilization of a pendulum --- p.109Chapter 6 --- MRAFC on a Class of Nonlinear Systems: Type II --- p.112Chapter 6.1 --- Introduction --- p.113Chapter 6.2 --- Fuzzy System as Function Approximator --- p.114Chapter 6.3 --- Construction of MRAFC for the nonlinear systems --- p.118Chapter 6.4 --- Input-Output Linearization --- p.130Chapter 6.5 --- MRAFC with Input-Output Linearization --- p.132Chapter 6.6 --- Example --- p.136Chapter 7 --- Analysis of MRAFC System --- p.140Chapter 7.1 --- Averaging technique --- p.140Chapter 7.2 --- Parameter convergence --- p.143Chapter 7.3 --- Robustness --- p.152Chapter 7.4 --- Simulation --- p.157Chapter 8 --- Application of MRAFC scheme on Manipulator Control --- p.166Chapter 8.1 --- Introduction --- p.166Chapter 8.2 --- Robot Manipulator Control --- p.170Chapter 8.3 --- MRAFC on Robot Manipulator Control --- p.173Chapter 8.3.1 --- Part A: Nonlinear-function feedback fuzzy controller --- p.174Chapter 8.3.2 --- Part B: State-feedback fuzzy controller --- p.182Chapter 8.4 --- Simulation --- p.186Chapter 9 --- Conclusion --- p.199Chapter A --- Implementation of MRAFC Scheme with Practical Issues --- p.203Chapter A.1 --- Rule Generation by MRAFC scheme --- p.203Chapter A.2 --- Implementation Considerations --- p.211Chapter A.3 --- MRAFC System Design Procedure --- p.215Bibliography --- p.21

Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer

In this paper, the adaptive fuzzy tracking control is proposed for a class of multi-input and multioutput (MIMO) nonlinear systems in the presence of system uncertainties, unknown non-symmetric input saturation and external disturbances. Fuzzy logic systems (FLS) are used to approximate the system uncertainty of MIMO nonlinear systems. Then, the compound disturbance containing the approximation error and the time-varying external disturbance that cannot be directly measured are estimated via a disturbance observer. By appropriately choosing the gain matrix, the disturbance observer can approximate the compound disturbance well and the estimate error converges to a compact set. This control strategy is further extended to develop adaptive fuzzy tracking control for MIMO nonlinear systems by coping with practical issues in engineering applications, in particular unknown non-symmetric input saturation and control singularity. Within this setting, the disturbance observer technique is combined with the FLS approximation technique to compensate for the effects of unknown input saturation and control singularity. Lyapunov approach based analysis shows that semi-global uniform boundedness of the closed-loop signals is guaranteed under the proposed tracking control techniques. Numerical simulation results are presented to illustrate the effectiveness of the proposed tracking control schemes

A New Approach to Nonlinear Tracking Control Based on Fuzzy Approximation

The problem of tracking control is addressed for a class of nonlinear systems with uncertainties. The original nonlinear systems are approximated by a fuzzy T-S model based on which a state-feedback controller is constructed by using the linear matrix inequalities. The approximating error is eliminated by an adaptive compensator based on fuzzy logic systems. The effectiveness of the proposed control scheme is demonstrated by a simulation example. The main advantage is that the designer makes milder constraint assumption for the approximation error and the uncertainties in nonlinear systems

Prescribed Performance Fuzzy Adaptive Output-Feedback Control for Nonlinear Stochastic Systems

A prescribed performance fuzzy adaptive output-feedback control approach is proposed for a class of single-input and single-output nonlinear stochastic systems with unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output-feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example is provided to show the effectiveness of the proposed approach

Robust Adaptive Fuzzy Output Tracking Control for a Class of Twin-Roll Strip Casting Systems

This paper is concerned with the adaptive fuzzy control problem for a class of twin-roll strip casting systems. By using fuzzy logic systems (FLSs) to approximate the compounded nonlinear functions, a novel robust output tracking controller with adaptation laws is designed based on the high gain observer. First, the nonlinear dynamic equations for the roll gap and the molten steel level are constructed, respectively. Then, the mean value theorem is employed to transform the nonaffine nonlinear systems to the corresponding affine nonlinear systems. Moreover, it is also proved that all the closed-loop signals are bounded and the systems output tracking errors can converge to the desired neighborhoods of the origin via the Lyapunov stability analysis. Finally, simulation results, based on semiexperimental system dynamic model and parameters, are worked out to show the effectiveness of the proposed adaptive fuzzy design method

Robust Adaptive Fuzzy Control of Uncertain Nonlinear Systems with Unknown Dead-Zone

Abstract This paper presents a robust adaptive fuzzy control scheme for a class of uncertain nonlinear systems containing an unknown dead-zone. Dead-zone characteristics are quite commonly encountered in actuators, such as hydraulic and pneumatic valves, electric servomotors, and electronic circuits, etc. Therefore, by using a description of a dead-zone and by exploring the properties of this dead-zone model intuitively and mathematically, a robust adaptive fuzzy control method is presented without constructing the dead-zone inverse. The unknown nonlinear functions of the controlled system are approximated by the fuzzy logic system according to some adaptive laws. By means of Lyapunov stability theorem, the proposed robust adaptive fuzzy control scheme can guarantee the robust stability of the whole closed-loop system with an unknown dead-zone in the actuator and obtain good tracking performance as well. Finally, an example and simulation results are illustrated to demonstrate the validity of the proposed method

Control of nonlinear systems using Sugeno fuzzy approximators

This thesis deals with the issue of controlling nonlinear systems by integrating available classical as well as modern tools such as fuzzy logic and neural networks. The proposed approaches throughout this thesis are based on the well known first-order Sugeno fuzzy system. To achieve a better understanding of the approximation and interpolation capabilities of Sugeno fuzzy system, the influence of the fuzzy set parameters and the reasoning method on the interpolation function of the fuzzy system is investigated. Control of nonlinear system based on known dynamic is considered first. A fuzzy gain scheduling approach is developed. The proposed approach is based on quasi-linear dynamic models of the plant. Classical optimal controllers for each set of operating conditions were developed. These controllers are used to construct a single fuzzy-logic gain scheduling-like controller. Adaptive-neuro-fuzzy inference system was used to construct the rules for the fuzzy gain schedule. This will guarantee the continuous change in the gains as the system parameters change in time or space. This procedure is systematic and can be used to design controllers for many nonlinear systems. Also, a modeling approach of some known types of static nonlinearities is proposed. Control of nonlinear system with unknown dynamic is also considered. An adaptive feedback control scheme for the tracking of a class of continuous-time plants is presented. A parameterized Sugeno fuzzy approximator is used to adaptively compensate for the plant nonlinearities. All parameters in the fuzzy approximator are tuned using a Luapunov-based design. In the fuzzy approximator, a first-order Sugeno consequent is used in the IF-THEN rules of the fuzzy system, which has a better approximation capability compared with that of a constant consequent. Global boundedness of the adaptive system is established. Finally, simulation and experimentation are used to demonstrate the effectiveness of the proposed controllers

Finite-Time Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems

This paper investigates the finite-time adaptive fuzzy tracking control problem for a class of pure-feedback system with full-state constraints. With the help of Mean-Value Theorem, the pure-feedback nonlinear system is transformed into strict-feedback case. By employing finite-time-stable like function and state transformation for output tracking error, the output tracking error converges to a predefined set in a fixed finite interval. To tackle the problem of state constraints, integral Barrier Lyapunov functions are utilized to guarantee that the state variables remain within the prescribed constraints with feasibility check. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions. In addition, all the signals in the closed-loop system are guaranteed to be semi-global ultimately uniformly bounded. Finally, two simulation examples are given to show the effectiveness of the proposed control strategy

Robust Adaptive Fuzzy Control for a Class of Uncertain MIMO Nonlinear Systems with Input Saturation

This paper studies the robust adaptive fuzzy control design problem for a class of uncertain multiple-input and multiple-output (MIMO) nonlinear systems in the presence of actuator amplitude and rate saturation. In the control scheme, fuzzy logic systems are used to approximate unknown nonlinear systems. To compensate the effect of input saturations, an auxiliary system is constructed and the actuator saturations then can be augmented into the controller. The modified tracking error is introduced and used in fuzzy parameter update laws. Furthermore, in order to deal with fuzzy approximation errors for unknown nonlinear systems and external disturbances, a robust compensation control is designed. It is proved that the closed-loop system obtains H∞ tracking performance through Lyapunov analysis. Steady and transient modified tracking errors are analyzed and the bound of modified tracking errors can be adjusted by tuning certain design parameters. The proposed control scheme is applicable to uncertain nonlinear systems not only with actuator amplitude saturation, but also with actuator amplitude and rate saturation. Detailed simulation results of a rigid body satellite attitude control system in the presence of parametric uncertainties, external disturbances, and control input constraints have been presented to illustrate the effectiveness of the proposed control scheme