Learning fuzzy inference systems using an adaptive membership function scheme

An adaptive membership function scheme for general additive fuzzy systems is proposed in this paper. The proposed scheme can adapt a proper membership function for any nonlinear input-output mapping, based upon a minimum number of rules and an initial approximate membership function. This parameter adjustment procedure is performed by computing the error between the actual and the desired decision surface. Using the proposed adaptive scheme for fuzzy system, the number of rules can be minimized. Nonlinear function approximation and truck backer-upper control system are employed to demonstrate the viability of the proposed method

A new approach to adaptive fuzzy control: the controller output error method

The controller output error method (COEM) is introduced and applied to the design of adaptive fuzzy control systems. The method employs a gradient descent algorithm to minimize a cost function which is based on the error at the controller output. This contrasts with more conventional methods which use the error at the plant output. The cost function is minimized by adapting some or all of the parameters of the fuzzy controller. The proposed adaptive fuzzy controller is applied to the adaptive control of a nonlinear plant and is shown to be capable of providing good overall system performance

Matrix formulation of fuzzy rule-based systems

In this paper, a matrix formulation of fuzzy rule based systems is introduced. A gradient descent training algorithm for the determination of the unknown parameters can also be expressed in a matrix form for various adaptive fuzzy networks. When converting a rule-based system to the proposed matrix formulation, only three sets of linear/nonlinear equations are required instead of set of rules and an inference mechanism. There are a number of advantages which the matrix formulation has compared with the linguistic approach. Firstly, it obviates the differences among the various architectures; and secondly, it is much easier to organize data in the implementation or simulation of the fuzzy system. The formulation will be illustrated by a number of examples

Hardware Implementation of a Mamdani Fuzzy Logic Controller for a Static Compensator in a Multimachine Power System

A Mamdani-type fuzzy logic controller is designed and implemented in hardware for controlling a static compensator (STATCOM), which is connected to a ten-bus multimachine power system. Such a controller does not need any mathematical model of the plant to be controlled and can efficiently provide control signals for the STATCOM over a wide range of operating conditions of the power system and during different disturbances. The proposed controller is implemented using the M67 digital signal processor board and is interfaced to the multimachine power system simulated on a real-time digital simulator. Experimental results are provided, showing that the proposed Mamdani fuzzy logic controller provides superior damping compared to the conventional proportional-integral (PI) controller for both small and large scale disturbances. In addition, the proposed controller manages to restore the power system to the steady state conditions with less control effort exerted by the STATCOM, which, in turn, leads to smaller megavar rating and, therefore, less cost for the device. The matrix pencil method analysis of the damping provided by the different controllers indicates that the proposed controller provides higher damping than the PI controller and also mitigates the modes present with the conventional PI control

Fully Evolvable Optimal Neurofuzzy Controller Using Adaptive Critic Designs

A near-optimal neurofuzzy external controller is designed in this paper for a static compensator (STATCOM) in a multimachine power system. The controller provides an auxiliary reference signal for the STATCOM in such a way that it improves the damping of the rotor speed deviations of its neighboring generators. A zero-order Takagi-Sugeno fuzzy rule base constitutes the core of the controller. A heuristic dynamic programming (HDP) based approach is used to further train the controller and enable it to provide nonlinear near-optimal control at different operating conditions of the power system. Based on the connectionist systems theory, the parameters of the neurofuzzy controller, including the membership functions, undergo training. Simulation results are provided that compare the performance of the neurofuzzy controller with and without updating the fuzzy set parameters. Simulation results indicate that updating the membership functions can noticeably improve the performance of the controller and reduce the size of the STATCOM, which leads to lower capital investment

Interval Type-2 Recurrent Fuzzy Neural System for Nonlinear Systems Control Using Stable Simultaneous Perturbation Stochastic Approximation Algorithm

This paper proposes a new type fuzzy neural systems, denoted IT2RFNS-A (interval type-2 recurrent fuzzy neural system with asymmetric membership function), for nonlinear systems identification and control. To enhance the performance and approximation ability, the triangular asymmetric fuzzy membership function (AFMF) and TSK-type consequent part are adopted for IT2RFNS-A. The gradient information of the IT2RFNS-A is not easy to obtain due to the asymmetric membership functions and interval valued sets. The corresponding stable learning is derived by simultaneous perturbation stochastic approximation (SPSA) algorithm which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results for the chaotic system identification and the control of Chua's chaotic circuit are shown to illustrate the feasibility and effectiveness of the proposed method