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This paper introduces a new chaotic jerk system with three cubic nonlinear terms. The stability properties of the three equilibrium points of the proposed jerk system are analyzed in detail. We show that the three equilibrium points of the new chaotic jerk system are unstable and deduce that the jerk system exhibits self-excited chaotic attractors. The bifurcation structures of the proposed jerk system are investigated numerically, showing period-doubling, periodic windows and coexisting bifurcations. An electronic circuit design of the proposed jerk system is designed using PSPICE. As an engineering application, a new image-encryption approach based on the new chaotic jerk system is presented in this research work. Experimental results demonstrate that the suggested encryption mechanism is effective with high plain-image sensitivity and the reliability of the proposed chaotic jerk system for various cryptographic purposes.

In this paper, a nonlinear Josephson junction (JJ) based-Wien bridge circuit is analyzed and coupled in order to obtain synchronization through passive components. The electrical equations governing the operation of our circuit are obtained using the laws of electrical circuit analysis. Chaotic phenomenon is demonstrated in the proposed circuit using relevant indicators such as the phase portraits, bifurcation and the corresponding Lyapunov diagram. Several coupling topologies are considered to achieve the phase synchronization that provides a better understanding of the distribution of energy in the overall system. Additionally, the effect of the noise is considered which considerably brings an added value to the dynamic of the phase synchronization between oscillators. Full synchronization is observed when the resistor is connected in parallel with the inductor or capacitor while different results are obtained when the resistor is connected in series with the capacitor or inductor. Finally, fine-tuning and selection of coupling coefficients reflects a migration toward synchronization between two Josephson junction based-Wien circuits that imply the self-adaptation of the synapse when two types of synapses are active simultaneously.

With renewable energy currently making the headlines, photovoltaic technology has shown significant potential as one of the best energy sources. It thus becomes necessary to predict the performance of photovoltaic systems by modeling it accurately and optimally. We propose a new hybrid algorithm for extracting PV cell parameters to improve their performance and efficiency when subjected to temperature variations. A metaheuristic approach is combined with an analytical approach to improve the accuracy and robustness. We call this approach improved differential evolution (IDE). The performance of the proposed method is evaluated for selected cell data. For validation, several analyses and comparisons are made with other methods, and the results illustrate the accuracy and precision of IDE. The proposed technique can estimate the parameters in an optimal way at any temperature, together with high convergence speed and a short simulation time.

This paper focuses on the problem of robust fuzzy sliding mode synchronization of uncertain nonlinear systems. A relevant fuzzy sliding mode control(FSMC) law is designed to force the state errors onto the specified surface. The prescribed-time boundedness (PTB) of the dynamical error is guaranteed by introducing the partitioning strategy. The chattering phenomenon, which is inherent to a conventional sliding mode control, is avoided by proper fuzzy tuning of the reaching law. The control law is deduced from the stability analysis of th closed-loop system in the sense of lyapunov. Furthermore, robustness issue is investigated and a prescribed-time property is obtained with sufficient conditions, established in terms of linear matrix inequalities (LMIs) using Lyapunov and cost functions. The results obtained show the effectiveness of the proposed control scheme and the reachability of the synchronization before the fixed time. The outcomes of this research are illustrated using computer simulations for the control problem of chaotic Chua’s system, in the presence of uncertainties, which clearly reveals that FSMC is better than SMC in terms of robustness. The present proposal provides a consistent procedure to design FSMC for a general class of nonlinear systems.

This paper mainly focuses on the robust synchronization of switched fractional-order improved Rikitake two-disk dynamo system which is a more general topology of the original Rikitake system. In particular, we first explore and design a simplified model very close to a real geophysical process which is described by an orbiting point, primarily using concepts from dynamical system theory. Dynamical properties, including symmetry, dissipation, stability of equilibria, Lyapunov exponents, and bifurcation, are analyzed on the basis of theoretical analysis and numerical simulation. Secondly, some less stringent conditions for adaptive control are derived when the system is subjected to external disturbances, parametric uncertainties and nonlinear input. The convergence of the state space trajectories with the overall robust asymptotic stability of the closed-loop system is obtained using the Lyapunov theory. To highlight our contribution, an illustrative example is presented to show the effectiveness and applicability of the proposed synchronization scheme. This proposal derives a systematic procedure for the design and control of a wide range of electromechanical systems. The results obtained in this work have not yet been reported in the literature to the best of the authors’ knowledge and thus deserve dissemination.

This paper deals with the modeling and theoretical study of an average-current-mode-controlled photovoltaic power conversion chain. It should be noted that current mode control is a superior scheme for controlling DC–DC power electronic converters for photovoltaic applications. Bifurcation diagrams, largest Lyapunov exponents, Floquet theory, and time series are used to study the dynamics of the system. The theoretical results show the existence of subharmonic oscillations and period-1 oscillations in the system. The results of the numerical simulations showed that when the battery voltage at the output of the converter is fixed and ramp amplitude is taken as a control parameter, the photovoltaic power system exhibits the phenomenon of period doubling leading to chaotic dynamics. Furthermore, bifurcation diagrams showed that both the critical value of ramp amplitude for the occurrence of border collision bifurcation and the critical value of ramp amplitude for the occurrence of period-1 in the proposed system increased with the value of the battery terminal voltage. The numerical results are in accordance with the theoretical ones. Finally, an external control based on a non-adaptive controller having a sinusoidal function as a target is applied to the overall system for the suppression of chaotic behavior.

The presence of a high ripple in the inductor current of a DC-DC converter in a photovoltaic converter chain leads to a considerable decrease in the energy efficiency of the converter. To solve this problem, we consider a current-mode control and for economic reasons we used a single inductor current sensor with a low-pass filter. The purpose of the low-pass filter is to minimize the effect of ripple in the inductor current by taking only the DC component of the signal at the output of the sensor for tracking the maximum power point. The objective of this paper is therefore to study the stability of the photovoltaic system as a function of the filter frequency while maintaining a good power level. First, we propose a general modeling of the whole system by linearizing the PV around the maximum power point. Floquet theory is used to determine analytically the stability of the overall system. The fourth-order Runge–Kutta method is used to plot bifurcation diagrams and Lyapunov exponents in MATLAB/SIMULINK when the filter frequency varies in a limited range and the ramp amplitude is taken as a control parameter. Secondly, the PSIM software is used to design the device and validate the results obtained in MATLAB/SIMULINK. The results depicted in MATLAB/SIMULINK are in perfect agreement with those obtained in PSIM. We found that not only is the energy level maintained at the maximum power level of 85.17 W, but also that the stability range of the photovoltaic system increased with the value of the filter cut-off frequency. This research offers a wider range of parameters for stability control of photovoltaic systems contrarily to others found in literature.

A robust polynomial observer is designed based on passive synchronization of a given class of fractional-order Colpitts (FOC) systems with mismatched uncertainties and disturbances. The primary objective of the proposed observer is to minimize the effects of unknown bounded disturbances on the estimation of errors. A more practicable output-feedback passive controller is proposed using an adaptive polynomial state observer. The distributed approach of a continuous frequency of the FOC is considered to analyze the stability of the observer. Then we derive some stringent conditions for the robust passive synchronization using Finsler’s lemma based on the fractional Lyapunov stability theory. It is shown that the proposed method not only guarantees the asymptotic stability of the controller but also allows the derived adaptation law to remove the uncertainties within the nonlinear plant’s dynamics. The entire system using passivity is implemented with details in PSpice to demonstrate the feasibility of the proposed control scheme. The results of this research are illustrated using computer simulations for the control problem of the fractional-order chaotic Colpitts system. The proposed approach depicts an efficient and systematic control procedure for a large class of nonlinear systems with the fractional derivative.

This paper focuses on the dynamical analysis of the permanent magnet asynchronous motor with the aim of subsequently designing effective robust control laws for the indirect field-oriented control (IFOC) devices. We first perform some tasks which demonstrate the existence of chaos phenomenon in the IFOC using relevant indicators such as phase portraits, bifurcations diagrams and Lyapunov exponents. Chaotic signature and some striking transitions are revealed such as period-doubling, torus, period-adding and chaos when an accessible parameter of the IFOC motor is changed. More interestingly, a certain range of the parameter space corresponds to the transient chaos. This behavior was not reported previously and can be considered as an enriching contribution. Secondly, due to the great interest to reduce the upper bound of uncertainties and interference, conventional sliding mode control (SMC) has been abundantly investigated for fault-tolerant control (FTC) systems. However, this approach presents several drawbacks in terms of overshoot, less robustness, transient state error, large chattering and speed of convergence that limit its use for industrial applications. For these reasons, the integral sliding mode control (ISMC) and the fuzzy sliding mode control (FISMC) are proposed to keep the IFOC motor in the regular operation zone. The optimal feedback gains and a sufficient condition are proposed for the stability of the overall IFOC system is drawn based on the linear quadratic regulator (LQR) method. To highlight the effectiveness and applicability of the proposed control scheme, numerical simulation results are presented. This analysis allows us a great knowledge of engineers for interpreting the operation of the IFOC motor. To highlight the effectiveness and the applicability of the proposed control scheme, numerical simulations results are presented and clearly demonstrated the feasibility of these techniques.