The structure of canalizing functions

The structure of a canalizing function is discussed. Using a new matrix product, namely semitensor product, the logical function is expressed in its matrix form. From its matrix expression, a criterion is obtained to test whether a logical function is a canalizing function. Then a formula is obtained to calculate the number of canalizing functions. Moreover, an algorithm is presented to generate canalizing functions. Finally, some results obtained are extended to seminested canalizing functions.     

Development of a sequential robust–tolerance design model for a destructive quality characteristic

Robust design (RD) and tolerance design (TD) have received much attention from researchers and practitioners for more than two decades, and a number of methodologies for modeling and optimizing the RD and TD processes have been studied. However, there is ample room for improvement. Because most existing research considers RD and TD as separate research fields, the primary objective of this paper is to develop a sequential robust–tolerance design method to jointly determine the best factor settings and the closed-form solutions for the optimal specification limits. We then apply the proposed method to a destructive quality characteristic. Finally, a case study and sensitivity analyses are performed for verification purposes, and further studies are discussed.     

Numerical method using cubic B-spline for the heat and wave equation

In the present paper, the cubic B-splines method is considered for solving one-dimensional heat and wave equations. A typical finite difference approach had been used to discretize the time derivative while the cubic B-spline is applied as an interpolation function in the space dimension. The accuracy of the method for both equations is discussed. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.     

Fault tolerant machine learning for nanoscale cognitive radio

We introduce a machine learning-based classifier that identifies free radio channels for cognitive radio. The architecture is designed for nanoscale implementation, under nanoscale implementation constraints; we do not describe all physical details but believe future physical implementation to be feasible. The system uses analog computation and consists of cyclostationary feature extraction and a radial basis function network for classification. We describe a model for nanoscale faults in the system, and simulate experimental performance and fault tolerance in recognizing WLAN signals, under different levels of noise and computational errors. The system performs well under expected non-ideal manufacturing and operating conditions.     

Dynamical systems identification using Gaussian process models with incorporated local models

Gaussian process (GP) models form an emerging methodology for modelling nonlinear dynamic systems which tries to overcome certain limitations inherent to traditional methods such as e.g. neural networks (ANN) or local model networks (LMN).The GP model seems promising for three reasons. First, less training parameters are needed to parameterize the model. Second, the variance of the model's output depending on data positioning is obtained. Third, prior knowledge, e.g. in the form of linear local models can be included into the model. In this paper the focus is on GP with incorporated local models as the approach which could replace local models network.Much of the effort up to now has been spent on the development of the methodology of the GP model with included local models, while no application and practical validation has yet been carried out. The aim of this paper is therefore twofold. The first aim is to present the methodology of the GP model identification with emphasis on the inclusion of the prior knowledge in the form of linear local models. The second aim is to demonstrate practically the use of the method on two higher order dynamical systems, one based on simulation and one based on measurement data.     

A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems

This paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for Takagi-Sugeno (TS) systems. This approach is based on the idea of multiple Lyapunov functions together with simple techniques for introducing slack matrices. Unlike some previous approaches based on multiple Lyapunov functions, both the stability and the stabilization conditions are written as linear matrix inequality (LMI) problems. The proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the LMI problems. Numeric examples illustrate the effectiveness of this method.     

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

This paper addresses the stability issue of discrete-time switched systems with guaranteed dwell-time. The approach of switched homogeneous Lyapunov function of higher order is formally proposed. By means of this approach, a necessary and sufficient condition is established to check the exponential stability of the considered system. With the observation that switching signal is actually arbitrary if the dwell time is one sample time, a necessary and sufficient condition is also presented to verify the exponential stability of switched systems under arbitrary switching signals. Using the augmented argument, a necessary and sufficient exponential stability criterion is given for discrete-time switched systems with delays. A numerical example is provided to show the advantages of the theoretical results.     

Stochastic system transformation using generalized orthonormal basis functions with applications to continuous-time system identification

This paper studies the system transformation using generalized orthonormal basis functions that include the Laguerre basis as a special case. The transformation of the deterministic systems is studied in the literature, which is called the Hambo transform. The aim of the paper is to develop a transformation theory for stochastic systems. The paper establishes the equivalence of continuous and transformed-discrete-time stochastic systems in terms of solutions. The method is applied to the continuous-time system identification problem. It is shown that using the transformed signals the PO-MOESP subspace identification algorithm yields consistent estimates for system matrices. An example is included to illustrate the efficacy of the proposed identification method, and to make a comparison with the method using the Laguerre filter.