Deterministic job-shop scheduling: Past, present and future

A technique for approximating a continuous function of n variables with a radial basis function (RBF) neural network is presented. The method uses an n-dimensional raised-cosine type of RBF that is smooth, yet has compact support. The RBF network coefficients are low-order polynomial functions of the input. A simple computational procedure is presented which significantly reduces the network training and evaluation time. Storage space is also reduced by allowing for a nonuniform grid of points about which the RBFs are centered. The network output is shown to be continuous and have a continuous first derivative. When the network is used to approximate a nonlinear dynamic system, the resulting system is bounded-input bounded-output stable. For the special case of a linear system, the RBF network representation is exact on the domain over which it is defined, and it is optimal in terms of the number of distinct storage parameters required. Several examples are presented which illustrate the effectiveness of this technique.

/pdf/approximation-of-nonlinear-systems-with-radial-basis-36h6xffs94.pdf

Approximation of nonlinear systems with radial basis function neural networks

In this paper, output feedback adaptive neural network (NN) controls are investigated for two classes of nonlinear discrete-time systems with unknown control directions: (1) nonlinear pure-feedback systems and (2) nonlinear autoregressive moving average with exogenous inputs (NARMAX) systems. To overcome the noncausal problem, which has been known to be a major obstacle in the discrete-time control design, both systems are transformed to a predictor for output feedback control design. Implicit function theorem is used to overcome the difficulty of the nonaffine appearance of the control input. The problem of lacking a priori knowledge on the control directions is solved by using discrete Nussbaum gain. The high-order neural network (HONN) is employed to approximate the unknown control. The closed-loop system achieves semiglobal uniformly-ultimately-bounded (SGUUB) stability and the output tracking error is made within a neighborhood around zero. Simulation results are presented to demonstrate the effectiveness of the proposed control.

/pdf/output-feedback-nn-control-for-two-classes-of-discrete-time-5ccp6i8xmn.pdf

Output Feedback NN Control for Two Classes of Discrete-Time Systems With Unknown Control Directions in a Unified Approach

In this paper, we investigate optimized adaptive control and trajectory generation for a class of wheeled inverted pendulum (WIP) models of vehicle systems Aiming at shaping the controlled vehicle dynamics to be of minimized motion tracking errors as well as angular accelerations, we employ the linear quadratic regulation optimization technique to obtain an optimal reference model Adaptive control has then been developed using variable structure method to ensure the reference model to be exactly matched in a finite-time horizon, even in the presence of various internal and external uncertainties The minimized yaw and tilt angular accelerations help to enhance the vehicle rider's comfort In addition, due to the underactuated mechanism of WIP, the vehicle forward velocity dynamics cannot be controlled separately from the pendulum tilt angle dynamics Inspired by the control strategy of human drivers, who usually manipulate the tilt angle to control the forward velocity, we design a neural-network-based adaptive generator of implicit control trajectory (AGICT) of the tilt angle which indirectly “controls” the forward velocity such that it tracks the desired velocity asymptotically The stability and optimal tracking performance have been rigorously established by theoretic analysis In addition, simulation studies have been carried out to demonstrate the efficiency of the developed AGICT and optimized adaptive controller

https://pearl.plymouth.ac.uk/bitstream/handle/10026.1/1301/SMCB13.pdf;sequence=2

Trajectory Planning and Optimized Adaptive Control for a Class of Wheeled Inverted Pendulum Vehicle Models

This paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks (RBFNNs) in order to approach target functions from a set of input-output pairs. The procedure allows the application of heuristics to improve the solution of the problem at hand by including some new genetic operators in the evolutionary process. These new operators are based on two well-known matrix transformations: singular value decomposition (SVD) and orthogonal least squares (OLS), which have been used to define new mutation operators that produce local or global modifications in the radial basis functions (RBFs) of the networks (the individuals in the population in the evolutionary procedure). After analyzing the efficiency of the different operators, we have shown that the global mutation operators yield an improved procedure to adjust the parameters of the RBFNNs.

https://sci2s.ugr.es/sites/default/files/files/TematicWebSites/GeneticFuzzySystems/2003-Gonzalez-IEEE_TNN.pdf

Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation

The problem of estimating an unknown function from a finite number of noisy data points has fundamental importance for many applications. This problem has been studied in statistics, applied mathematics, engineering, artificial intelligence, and, more recently, in the fields of artificial neural networks, fuzzy systems, and genetic optimization. In spite of many papers describing individual methods, very little is known about the comparative predictive (generalization) performance of various methods. We discuss subjective and objective factors contributing to the difficult problem of meaningful comparisons. We also describe a pragmatic framework for comparisons between various methods, and present a detailed comparison study comprising several thousand individual experiments. Our approach to comparisons is biased toward general (nonexpert) users. Our study uses six representative methods described using a common taxonomy. Comparisons performed on artificial data sets provide some insights on applicability of various methods. No single method proved to be the best, since a method's performance depends significantly on the type of the target function, and on the properties of training data.

D. Gehring

Papers

Comparison of adaptive methods for function estimation from samples