This paper aims to propose a self-triggered consensus control scheme for a class of nonlinear multi-agent systems with sensor saturation. Because of the existence of unknown nonlinear dynamics, this study borrows the approximation capability of neural networks to design the consensus control protocol. This paper adopts neural network to approximate the ideal controller, instead of using the combination of neural network and adaptive method to approximate the unknown system dynamics. Thus, the extended approximation property of neural network for event-based sampling can be beneficially introduced. Moreover, the designed controller only updates at discrete time, which enables that the system can be modeled as a hybrid system with impulsive dynamics. Thus, the stability theory of impulsive systems can be used to analyze the convergence of the system. It should be noted that this is the first time to propose an effective event-triggered consensus control algorithm based on neural network. Furthermore, this paper also considers a frequently encountered phenomenon of sensor saturation. The convex hull method is adopted to deal with sensor saturation problem, instead of the widely used sector condition method. Finally, the performance of the proposed neural-network based self-triggered consensus control algorithm is demonstrated by the numerical examples.

In this article, a class of uncertain nonstrict-feedback fractional-order nonlinear single-input-single-output (SISO) systems is investigated. Fuzzy-logic systems (FLSs) are employed to approximate the unknown nonlinear functions and model the uncertain fractional-order nonlinear systems. For the states measurable case, an adaptive fuzzy state-feedback control scheme is developed under the framework of the backstepping technique. For the states unmeasurable case, an observer-based output-feedback control design is proposed by introducing a serial-parallel estimation model and using the dynamic surface control (DSC) technique. Under the drive of the reference signals, the semiglobally uniformly ultimate boundedness for all signals and the tracking errors converging to a small neighborhood of the origin are proved based on the Lyapunov function theory by choosing appropriate design parameters. Two examples with numerical simulations are presented to illustrate the availability of the proposed control approaches.

Linear discriminant analysis (LDA) faces challenges in practical applications due to the small sample size (SSS) problem and high computational costs. Various solutions have been proposed to address the SSS problem in both ratio trace LDA and trace ratio LDA (TRLDA). However, the iterative processing of large matrices often makes the computation process cumbersome. To address this issue, for TRLDA, we propose a novel random method that extracts orthogonal bases from matrices, allowing computations with small-sized matrices. This significantly reduces computational time without compromising accuracy. For ratio trace LDA, we introduce a fast generalized singular value decomposition (GSVD) algorithm, which demonstrates superior speed compared to MATLAB’s built-in GSVD algorithm in experiments. By integrating this new GSVD algorithm into ratio trace LDA, we propose FGSVD-LDA, which exhibits low computational complexity and good classification performance. The experimental results show that both methods effectively achieve dimensionality reduction and deliver satisfactory classification accuracy.

Let $A\in\mathbb{C}^{m \times n}$ have generalized polar decomposition $A = QH$ with $Q$ subunitary and $H$ positive semidefinite. Absolute and relative perturbation bounds are derived for the subunitary polar factor $Q$ in unitarily invariant norms and in $Q$-norms, that extend and improve existing bounds.

Perturbation Bounds and Condition Numbers for a Complex Indefinite Linear Algebraic System - Volume 6 Issue 2 - Lei Zhu, Wei-Wei Xu, Xing-Dong Yang