Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated example

Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses

This paper is concerned with the H∞ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete-time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Attention is focused on the analysis and design of an observer-based feedback controller such that the closed-loop control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical result

System Identification for Nonlinear Control Using Neural Networks

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique

Time-delayed impulsive control for discrete-time nonlinear systems with actuator saturation

This paper focuses on the problem of time-delayed impulsive control with actuator saturation for discrete-time dynamical systems. By establishing a delayed impulsive difference inequality, combining with convex analysis and inequality techniques, some sufficient conditions are obtained to ensure exponential stability for discrete-time dynamical systems via time-delayed impulsive controller with actuator saturation. The designed controller admits the existence of some transmission delays in impulsive feedback law, and the control input variables are required to stay within an availability zone. Several numerical simulations are also given to demonstrate the effectiveness of the proposed results.&nbsp

Using rule extraction to improve the comprehensibility of predictive models.

Whereas newer machine learning techniques, like artifficial neural net-works and support vector machines, have shown superior performance in various benchmarking studies, the application of these techniques remains largely restricted to research environments. A more widespread adoption of these techniques is foiled by their lack of explanation capability which is required in some application areas, like medical diagnosis or credit scoring. To overcome this restriction, various algorithms have been proposed to extract a meaningful description of the underlying `blackbox' models. These algorithms' dual goal is to mimic the behavior of the black box as closely as possible while at the same time they have to ensure that the extracted description is maximally comprehensible. In this research report, we first develop a formal definition of`rule extraction and comment on the inherent trade-off between accuracy and comprehensibility. Afterwards, we develop a taxonomy by which rule extraction algorithms can be classiffied and discuss some criteria by which these algorithms can be evaluated. Finally, an in-depth review of the most important algorithms is given.This report is concluded by pointing out some general shortcomings of existing techniques and opportunities for future research.Models; Model; Algorithms; Criteria; Opportunities; Research; Learning; Neural networks; Networks; Performance; Benchmarking; Studies; Area; Credit; Credit scoring; Behavior; Time;

On the design of dynamic associative neural memories

Cataloged from PDF version of article.We consider the design problem for a class of discrete-time and continuous-time neural networks. We obtain a characterization of all connection weights that store a given set of vectors into the network; that is, each given vector becomes an equilibrium point of the network. We also give sufficient conditions that guarantee the asymptotic stability of these equilibrium points

Associative memory design using overlapping decompositions

Cataloged from PDF version of article.This paper discusses the use of decomposition techniques in the design of associative memories via arti"cial neural networks. In particular, a disjoint decomposition which allows an independent design of lower-dimensional subnetworks and an overlapping decomposition which allows subnetworks to share common parts, are analyzed. It is shown by a simple example that overlapping decompositions may help in certain cases where design by disjoint decompositions fails. With this motivation, an algorithm is provided to synthesize neural networks using the concept of overlapping decompositions. Applications of the proposed design procedure to a benchmark example from the literature and to a pattern recognition problem indicate that it may improve the e!ectiveness of the existing methods. ( 2001 Published by Elsevier Science Ltd

A Novel Self-organizing Fuzzy Cerebellar Model Articulation Controller Based Overlapping Gaussian Membership Function for Controlling Robotic System

This paper introduces an effective intelligent controller for robotic systems with uncertainties. The proposed method is a novel self-organizing fuzzy cerebellar model articulation controller (NSOFC) which is a combination of a cerebellar model articulation controller (CMAC) and sliding mode control (SMC). We also present a new Gaussian membership function (GMF) that is designed by the combination of the prior and current GMF for each layer of CMAC. In addition, the relevant data of the prior GMF is used to check tracking errors more accurately. The inputs of the proposed controller can be mixed simultaneously between the prior and current states according to the corresponding errors. Moreover, the controller uses a self-organizing approach which can increase or decrease the number of layers, therefore the structures of NSOFC can be adjusted automatically. The proposed method consists of a NSOFC controller and a compensation controller. The NSOFC controller is used to estimate the ideal controller, and the compensation controller is used to eliminate the approximated error. The online parameters tuning law of NSOFC is designed based on Lyapunov’s theory to ensure stability of the system. Finally, the experimental results of a 2 DOF robot arm are used to demonstrate the efficiency of the proposed controller