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

Real-valued feature selection for process approximation and prediction

The selection of features for classification, clustering and approximation is an important task in pattern recognition, data mining and soft computing. For real-valued features, this contribution shows how feature selection for a high number of features can be implemented using mutual in-formation. Especially, the common problem for mutual information computation of computing joint probabilities for many dimensions using only a few samples is treated by using the Rènyi mutual information of order two as computational base. For this, the Grassberger-Takens corre-lation integral is used which was developed for estimating probability densities in chaos theory. Additionally, an adaptive procedure for computing the hypercube size is introduced and for real world applications, the treatment of missing values is included. The computation procedure is accelerated by exploiting the ranking of the set of real feature values especially for the example of time series. As example, a small blackbox-glassbox example shows how the relevant features and their time lags are determined in the time series even if the input feature time series determine nonlinearly the output. A more realistic example from chemical industry shows that this enables a better ap-proximation of the input-output mapping than the best neural network approach developed for an international contest. By the computationally efficient implementation, mutual information becomes an attractive tool for feature selection even for a high number of real-valued features

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;

(t, k)-diagnosable system: A generalization of the PMC models

ln this paper, we introduce a new model for diagnosable systems called (t, k)-diagnosable system which guarantees that at least k faulty units (processors) in a system are detected provided that the number of faulty units does not exceed t. This system includes classical one-step diagnosable systems and sequentially diagnosable systems. We prove a necessary and sufficient condition for (t, k)-diagnosable system, and discuss a lower bound for diagnosability. Finally, we deal with a relation between (t, k)-diagnosability and diagnosability of classical basic models

Parallel Architectures for Planetary Exploration Requirements (PAPER)

The Parallel Architectures for Planetary Exploration Requirements (PAPER) project is essentially research oriented towards technology insertion issues for NASA's unmanned planetary probes. It was initiated to complement and augment the long-term efforts for space exploration with particular reference to NASA/LaRC's (NASA Langley Research Center) research needs for planetary exploration missions of the mid and late 1990s. The requirements for space missions as given in the somewhat dated Advanced Information Processing Systems (AIPS) requirements document are contrasted with the new requirements from JPL/Caltech involving sensor data capture and scene analysis. It is shown that more stringent requirements have arisen as a result of technological advancements. Two possible architectures, the AIPS Proof of Concept (POC) configuration and the MAX Fault-tolerant dataflow multiprocessor, were evaluated. The main observation was that the AIPS design is biased towards fault tolerance and may not be an ideal architecture for planetary and deep space probes due to high cost and complexity. The MAX concepts appears to be a promising candidate, except that more detailed information is required. The feasibility for adding neural computation capability to this architecture needs to be studied. Key impact issues for architectural design of computing systems meant for planetary missions were also identified

Adaptive fault-tolerant routing in hypercube multicomputers

A connected hypercube with faulty links and/or nodes is called an injured hypercube. To enable any non-faulty node to communicate with any other non-faulty node in an injured hypercube, the information on component failures has to be made available to non-faulty nodes so as to route messages around the faulty components. A distributed adaptive fault tolerant routing scheme is proposed for an injured hypercube in which each node is required to know only the condition of its own links. Despite its simplicity, this scheme is shown to be capable of routing messages successfully in an injured hypercube as long as the number of faulty components is less than n. Moreover, it is proved that this scheme routes messages via shortest paths with a rather high probabiltiy and the expected length of a resulting path is very close to that of a shortest path. Since the assumption that the number of faulty components is less than n in an n-dimensional hypercube might limit the usefulness of the above scheme, a routing scheme is introduced based on depth-first search which works in the presence of an arbitrary number of faulty components. Due to the insufficient information on faulty components, the paths chosen by the above scheme may not always be the shortest. To guarantee that all messages be routed via shortest paths, it is proposed that every mode be equipped with more information than that on its own links. The effects of this additional information on routing efficiency are analyzed, and the additional information to be kept at each node for the shortest path routing is determined. Several examples and remarks are also given to illustrate the results

Star varietal cube: A New Large Scale Parallel Interconnection Network

This paper proposes a new interconnection network topology, called the Star varietalcube SVC(n,m), for large scale multicomputer systems. We take advantage of the hierarchical structure of the Star graph network and the Varietal hypercube to obtain an efficient method for constructing the new topology. The Star graph of dimension n and a Varietal hypercube of dimension m are used as building blocks. The resulting network has most of the desirable properties of the Star and Varietal hypercube including recursive structure, partionability, strong connectivity. The diameter of the Star varietal hypercube is about two third of the diameter of the Star-cube. The average distance of the proposed topology is also smaller than that of the Star-cube