Fawaz E. Alsaadi

The Global Exponential Stability of the Delayed Complex-Valued Neural Networks with Almost Periodic Coefficients and Discontinuous Activations

In this paper, the almost periodic dynamical behaviors are considered for delayed complex-valued neural networks with discontinuous activation functions. We decomposed complex-valued to real and imaginary parts, and set an equivalent discontinuous right-hand equation. Depended on the differential inclusions theory, diagonal dominant principle, non-smooth analysis theory and generalized Lyapunov function, sufficient criteria are obtained for the existence uniqueness and global stability of almost periodic solution of the equivalent delayed differential system. Especially, we derive a series of results on the equivalent neural networks with discontinuous activations and periodic coefficients or constant coefficients, respectively. Finally, we give one numerical example to demonstrate the effectiveness of the derived theoretical results.

Optimal adaptive higher order controllers subject to sliding modes for a carrier system

Due to costly space projects, affordable flight models and test prototypes are of incomparable importance in academic and research applications, for example, data acquisition and subsystems testing. In this regard, CanSat could be used as a low-cost, high-tech, and lightweight model. CanSat carrier launch system is a simple second-order aerospace system. Aerospace systems require the highest level of effective controller performance. Adding second-order integral and second-order derivative terms to proportional–integral–derivative controller leads to the elimination of steady-state errors and yields to a faster systems convergence. Moreover, sliding mode control is considered as a robust controller that has appropriate features to track. Thus, this article tends to present an adaptive hybrid of higher order proportional–integral–derivative and sliding mode control optimized by multi-objective genetic algorithm to control a CanSat carrier launch system.

Fractional Form of a Chaotic Map without Fixed Points: Chaos, Entropy and Control

In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase plots and bifurcation diagrams to examine the dynamics of the fractional map and assess the effect of varying the fractional order. We also use the approximate entropy measure to quantify the level of chaos in the fractional map. In addition, we propose a one-dimensional stabilization controller and establish its asymptotic convergence by means of the linearization method.

A New Chaotic System with Stable Equilibrium: Entropy Analysis, Parameter Estimation, and Circuit Design

In this paper, we introduce a new, three-dimensional chaotic system with one stable equilibrium. This system is a multistable dynamic system in which the strange attractor is hidden. We investigate its dynamic properties through equilibrium analysis, a bifurcation diagram and Lyapunov exponents. Such multistable systems are important in engineering. We perform an entropy analysis, parameter estimation and circuit design using this new system to show its feasibility and ability to be used in engineering applications.

Intermittent Control for Cluster-Delay Synchronization in Directed Networks

We investigate cluster-delay synchronization of a directed network possessing cluster structures by designing an intermittent control protocol. Based on Lyapunov stability theory, we proved that synchronization can be realized for oscillators in the same cluster and cluster-delay synchronization can be realized for the whole network. By simplifying the obtained sufficient conditions, we carry out a succinct and utilitarian corollary. In addition, comparative researches are carried out to show the differences and the usefulness of the obtained results with respect to other similar controllers from the recent literature. Finally we provide two numerical examples to show the effectiveness of the control schemes.

Parameter Identification and Adaptive Control of Uncertain Goodwin Oscillator Networks with Disturbances

This paper investigates the dynamic properties of a differential equation model of mammals’ circadian rhythms, including parameter identification, adaptive control, and outer synchronization. The circadian oscillator network is described by a Goodwin oscillator network, the couplings of which are from vasoactive intestinal polypeptides described by modified Van der Pol oscillators. We build up a drive-response system consisting of two networks with unknown parameters and disturbances. Then, we propose effective parameter updating laws to identify the unknown parameters and design adaptive control strategies to achieve outer synchronization in the drive-response system. As special cases, two succinct corollaries are presented for different instances. All the theoretical results are proved through strict mathematical deduction based on Lyapunov stability theory, and a numerical example is also carried out to illustrate the effectiveness.

Dynamic system with no equilibrium and its chaos anti-synchronization

ABSTRACT Recently, systems with chaos and the absence of equilibria have received a great deal of attention. In our work, a simple five-term system and its anti-synchronization are presented. It is special that the system has a hyperbolic sine nonlinearity and no equilibrium. Such a system generates chaotic behaviours, which are verified by phase portraits, positive Lyapunov exponent as well as an electronic circuit. Moreover, the system displays multistable characteristic when changing its initial conditions. By constructing an adaptive control, chaos anti-synchronization of the system with no equilibrium is obtained and illustrated via a numerical example.