Fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control are reviewed. The essential part of neuro-fuzzy synergisms comes from a common framework called adaptive networks, which unifies both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (Adaptive-Network-based Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neuro-fuzzy approaches are also addressed.

Radial Basis Functions (RBF) consists of a two-layer neural network, where each hidden unit implements a kernel function. Each kernel is associated with an activation region from the input space and its output is fed to an output unit. In order to find the parameters of a neural network which embeds this structure we take into consideration two different statistical approaches. The first approach uses classical estimation in the learning stage and it is based on the learning vector quantization algorithm and its second order statistics extension. After the presentation of this approach, we introduce the Median Radial Basis Functions (MRBF) algorithm based on robust estimation of the hidden unit parameters. The proposed algorithm employs the marginal median for kernel location estimation and the median of the absolute deviations for the scale parameter estimation. A histogram-based fast implementation is provided for the MRBF algorithm. The theoretical performance of the two training al...

We consider adaptive output feedback control of uncertain nonlinear sy[q6M3 in which both the dy6Mq1g and the dimension of the regulated plant may be unknown.Only knowledge of relative degree is assumed. Given a smooth reference trajectory , the problem is to design a controller that forces the syM9q measurement to track it with bounded errors. The classical approach necessitates buildinga state observer. However, findinga good observer for an uncertain nonlinear syM[9 is not an obvious task. We argue that it should be su#cient to build an observer for the output trackingerror. Ultimate boundedness of the error signals is shown through Ly apunov like stability analyqqg The method is illustrated in the design of a controller for a fourth order nonlinear syM99 of relative degree 2 and a high-bandwidth attitude command symma for a model R-50 helicopter. 1 Introdu-88/ Research in adaptive output feedback control of uncertain nonlinear sy[q#6 is motivated by the many emerging applications that employ novel actuation devices for active control of flexible structures, fluid flows and combustion processes. These include such devices as piezo electric films, andsy thetic jets, which are ty pically nonlinearly coupled to the dy[M11q of the processes they are intended to control. Modelingfor these applications vary from havingaccurate low frequency models in the case of structural control problems, to havingno reasonable set of model equations in the case of active control of flows and combustion processes. Regardless of the extent of the model accuracy that may be present, an important aspect in any control design is the e#ect of parametric uncertainty and unmodeleddydg#q69 While it can be said the issue of parametric uncertainty is addressed within the context of adaptive cont...

Abstract—Consider the problem of developing a controller for general (nonlinear and stochastic) systems where the equations governing the system are unknown. Using discrete-time measurements, this paper presents an approach for estimating a controller without building or assuming a model for the system (including such general models as differential/difference equations, neural networks, fuzzy logic rules, etc.). Such an approach has potential advantages in accommodating complex systems with possibly time-varying dynamics. Since control requires some mapping, taking system information, and producing control actions, the controller is constructed through use of a function approximator (FA) such as a neural network or polynomial (no FA is used for the unmodeled system equations). Creating the controller involves the estimation of the unknown parameters within the FA. However, since no functional form is being assumed for the system equations, the gradient of the loss function for use in standard optimization algorithms is not available. Therefore, this paper considers the use of the simultaneous perturbation stochastic approximation algorithm, which requires only system measurements (not a system model). Related to this, a convergence result for stochastic approximation algorithms with time-varying objective functions and feedback is established. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations. Index Terms — Direct adaptive control, gradient estimation, nonlinear systems, simultaneous perturbation stochastic approximation. I.

This paper presents a direct adaptive output feedback design procedure. The design employs feedback linearization, coupled with an on-line NN to compensate for modeling errors. A xed structure dynamic compensator is designed to stabilize the linearized system. A signal, comprised of a linear combination of the measured tracking error and the compensator states, is used to adapt the NN weights. The input vector to the NN is composed of current and past input/output data. The control system is augmented byalow-pass lter designed to satisfy a strictly positive real (SPR) condition of a transfer function associated with the Lyapunov stability analysis. The stability analysis is used to construct the NN adaptation law using only available measurement as a training signal, and to prove boundedness of all the error signals of the closed loop system. A numerical example consisting of a Van del Pol oscillator coupled to a linear oscillator is treated to illustrate the robustness of the design approach with respect to both parametric uncertainty and unmodeled dynamics. 2 Problem Statement Let the dynamics of an observable nonlinear single-input-single-output (SISO) system be given by the following equations: _ x = #(x##)# # = #(x) (1) where x

In this paper, adaptive control of a class of nonlinear discrete time dynamical systems with boundedness of all signals is established by using a linear robust adaptive controller and a neural network based nonlinear adaptive controller, and switching between them by a suitably defined switching law. The linear controller, when used alone, assures boundedness of all the signals but not satisfactory performance. The nonlinear controller may result in improved response, but may also result in instability. By using a switching scheme, it is demonstrated that improved performance and stability can be simultaneously achieved. Key words: nonlinear control, adaptive control, neural networks, multiple models, switching systems, stability, robustness, performance 1

The design and analysis of fault diagnosis architectures using the model-based analytical redundancy approach has received considerable attention during the last two decades. One of the key issues in the design of such fault diagnosis schemes is the effect of modeling uncertainties on their performance. This paper describes a fault diagnosis algorithm for a class of nonlinear dynamic systems with modeling uncertainties when not all states of the system are measurable. The main idea behind this approach is to monitor the plant for any off-nominal system behavior due to faults utilizing a nonlinear on-line approximator with adjustable parameters. The on-line approximator only uses the system input and output measurements. A nonlinear estimation model and learning algorithm are described so that the on-line approximator provides an estimate of the fault. The robustness, sensitivity, stability and performance properties of the nonlinear fault diagnosis scheme are rigorously established und...

Previous work has provided the theoretical foundations of a constructive design procedure for uniform approximation of smooth functions to a chosen degree of accuracy using networks of gaussian radial basis functions. This construction and the guaranteed uniform bounds were then shown to provide the basis for stable adaptive neurocontrol algorithms for a class of nonlinear plants. This paper details and extends these ideas in three directions: first some practical details of the construction are provided, explicitly illustrating the relation between the free parameters in the network design and the degree of approximation error on a particular set. Next, the original adaptive control algorithm is modified to permit incorporation of additional prior knowledge of the system dynamics, allowing the neurocontroller to operate in parallel with conventional fixed or adaptive controllers. Finally, it is shown how the gaussian network construction may also be utilized in recursive identificatio...

Due to their powerful optimization property, genetic algorithms (GAs) are currently being investigated for the development of adaptive or self-tuning fuzzy logic control systems. This paper presents a neuro-fuzzy logic controller (NFLC) where all of its parameters can be tuned simultaneously by GA. The structure of the controller is based on the Radial Basis Function neural network (RBF) with Gaussian membership functions. The NFLC tuned by GA can somewhat eliminate laborious design steps such as manual tuning of the membership functions and selection of the fuzzy rules. The GA implementation incorporates dynamic crossover and mutation probabilistic rates for faster convergence. A flexible position coding strategy of the NFLC parameters is also implemented to obtain near optimal solutions. The performance of the proposed controller is compared with a conventional fuzzy controller and a PID controller tuned by GA. Simulation results show that the proposed controller offers encouraging advantages and has better performance.

In this paper we consider the problem of approximating a function belonging to some function space \Phi by a linear combination of n translates of a given function G.