Jason Sheng Hong Tsai

An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays

Based on the linear matrix inequality method, we introduce the robust stability of uncertain linear stochastic differential delay systems with delay dependence. The parameter uncertainty is norm-bounded and the delays are time varying. We then extend the proposed theory to discuss the robust stabilization of uncertain stochastic differential delay systems.

Stability of cellular neural networks with time-varying delay

The stability for cellular neural networks (CNNs) with time-varying delay is introduced by using a linear-matrix inequality. A sufficient condition related to the global asymptotic stability for delay CNNs is proposed. It is shown that the condition relies on the dependence of the delay. This condition is less restrictive than that given in the literature.

A boundary method for outlier detection based on support vector domain description

The support vector domain description (SVDD) is a popular kernel method for outlier detection, which tries to fit a class of data with a sphere and uses a few target objects to support its decision boundary. The problem is that even with a flexible Gaussian kernel function, the SVDD could sometimes generate such a loose decision boundary that the discrimination ability becomes poor. Therefore, a computationally intensive procedure called kernel whitening is often required to improve the performance. In this paper, we propose a simple post-processing method which tries to modify the SVDD boundary in order to achieve a tight data description with no need of kernel whitening. With the derivation of the distance between an object and its nearest boundary point in input space, the proposed method can efficiently construct a new decision boundary based on the SVDD boundary. The improvement from the proposed method is demonstrated with synthetic and real-world datasets. The results show that the proposed decision boundary can fit the shape of synthetic data distribution closely and achieves better or comparable classification performance on real-world datasets.

Improving Differential Evolution With a Successful-Parent-Selecting Framework

An effective and efficient successful-parent-selecting framework is proposed to improve the performance of differential evolution (DE) by providing an alternative for the selection of parents during mutation and crossover. The proposed method adapts the selection of parents by storing successful solutions into an archive, and the parents are selected from the archive when a solution is continuously not updated for an unacceptable amount of time. The proposed framework provides more promising solutions to guide the evolution and effectively helps DE escaping the situation of stagnation. The simulation results show that the proposed framework significantly improves the performance of two original DEs and six state-of-the-art algorithms in four real-world optimization problems and 30 benchmark functions.

A Delay-Dependent Approach to Passivity Analysis for Uncertain Neural Networks with Time-varying Delay

This paper deals with the problem of passivity analysis for neural networks with time-varying delay, which is subject to norm-bounded time-varying parameter uncertainties. The activation functions are supposed to be bounded and globally Lipschitz continuous. Delay-dependent passivity condition is proposed by using the free-weighting matrix approach. These passivity conditions are obtained in terms of linear matrix inequalities, which can be investigated easily by using standard algorithms. Two illustrative examples are provided to demonstrate the effectiveness of the proposed criteria.

A self-optimization approach for L-SHADE incorporated with eigenvector-based crossover and successful-parent-selecting framework on CEC 2015 benchmark set

A self-optimization approach and a new success-history based adaptive differential evolution with linear population size reduction (L-SHADE) which is incorporated with an eigenvector-based (EIG) crossover and a successful-parent-selecting (SPS) framework are proposed in this paper. The EIG crossover is a rotationally invariant operator which provides superior performance on numerical optimization problems with highly correlated variables. The SPS framework provides an alternative of the selection of parents to prevent the situation of stagnation. The proposed SPS-L-SHADE-EIG combines the L-SHADE with the EIG and SPS frameworks. To further improve the performance, the parameters of SPS-L-SHADE-EIG are self-optimized in terms of each function under IEEE Congress on Evolutionary Computation (CEC) benchmark set in 2015. The stochastic population search causes the performance of SPS-L-SHADE-EIG noisy, and therefore we deal with the noise by re-evaluating the parameters if the parameters are not updated for more than an unacceptable amount of times. The experiment evaluates the performance of the self-optimized SPS-L-SHADE-EIG in CEC 2015 real-parameter single objective optimization competition.

Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix sector function

This paper presents rapidly convergent and more stable recursive algorithms for finding the principal nth root of a complex matrix and the associated matrix sector function. The developed algorithms significantly improve the computational aspects of finding the principal nth root of a matrix and the matrix sector function. Thus, the developed algorithms will enhance the capabilities of the existing computational algorithms such as the principal nth root algorithm, the matrix sign algorithm and the matrix sector algorithm for developing applications to control system problems.

Determining continuous-time state equations from discrete-time state equations via the principal q th root method

Fast computational methods are developed for finding the equivalent continuous-time state equations from discrete-time state equations. The computational methods utilize the direct truncation method, the matrix continued fraction method, and the geometric-series method in conjunction with the principal q th root of the discrete-time system matrix for quick determination of the approximants of a matrix logarithm function. It is shown that the use of the principal q th root of a matrix enables us to enlarge the convergence region of the expansion of a matrix logarithm function and to improve the accuracy of the approximants of the matrix logarithm function.

Discretized quadratic optimal control for continuous-time two-dimensional systems

In this paper, discretized quadratic optimal control for continuous-time two-dimensional (2D) systems is newly proposed. It introduces a new state vector (a new virtual control input) to directly convert the original continuous-time 2D quadratic cost function into a decoupled discretized form. As a result, a new virtual discrete-time 2D model with the new virtual control input is constructed to indirectly find the desired discretized quadratic optimal regulator for the continuous-time 2D system. The recently developed dynamic programming in discrete-time 1D descriptor form is utilized to determine the desired discretized quadratic optimal regulator. This method provides a novel approach for discretized quadratic optimal control of continuous-time 2D systems. An illustrative example is presented to demonstrate the effectiveness of the proposed procedure.

Digital redesign of H8 controller via bilinear approximation method for state-delayed systems

Two issues are addressed: digitial modeling of the continuous-time state-delayed system; and digital redesign of the observer-based H8 controller for the continuous-time state-delayed system. The b...