A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation

Abstract

This chapter announces a new four-dimensional hyperchaotic system having two positive Lyapunov exponents, a zero Lyapunov exponent, and a negative Lyapunov exponent. Since the sum of the Lyapunov exponents of the new hyperchaotic system is shown to be negative, it is a dissipative system. The phase portraits of the new hyperchaotic system are displayed with both two-dimensional and three-dimensional phase portraits. Next, the qualitative properties of the new hyperchaotic system are dealt with in detail. It is shown that the new hyperchaotic system has three unstable equilibrium points. Explicitly, it is shown that the equilibrium at the origin is a saddle-point, while the other two equilibrium points are saddle-focus equilibrium points. Thus, it is shown that all three equilibrium points of the new hyperchaotic system are unstable. Numerical simulations with MATLAB have been shown to validate and demonstrate all the new results derived in this chapter. Finally, a circuit design of the new hyperchaotic system is implemented in MultiSim to validate the theoretical model.

Photovoltaic Systems Based on Average Current Mode Control: Dynamical Analysis and Chaos Suppression by Using a Non-Adaptive Feedback Outer Loop Controller

“…For practical studies, this paper can then help to select values for which there is undesirable behavior. Since it has been shown in the literature that adaptive controllers are more robust than their non-adaptive counterparts [48][49][50], the application of an adaptive external controller to the PV system studied in this work, as well as the experimental implementation of the results obtained, will be the subject of future work.…”

“…Thus, our objective in this part will be to bring an external control to the system in order to make the control signal v con tend towards a sinusoidal voltage to destroy the subharmonic behavior in the photovoltaic system. Of all the control methods in the literature, we choose the nonadaptive control method because it is easy to implement and inexpensive [48][49][50]. Applying the non-adaptive controller to the internal controller block, Equation ( 5) becomes:…”

“…where k i i ∈ [1, 4] represents the non-adaptive feedback gains and the function f (t) = a 0 + a 1 sin(2πτ) represents the sinusoidal current (I * ) or the sinusoidal voltage (V * ) taken as the target to be achieved by i e , v e , i con , and v con . For practical and clutter reasons, it is advisable to control only one direction of the system to be monitored [48][49][50]. Thus, as it is the voltage v con that we are interested here, we choose to annul the gains k 1 , k 2 , and k 3 (the case of Figure 5).…”

Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control

“…Chaos theory represents a new field of research based on qualitative and empirical analysis of chaotic a periodic behavior [1][2][3][4][5][6][7]. A dynamic system is called chaotic when it fulfills the three characteristics of constraints, constant repetitions, and responsive dependent conditions.…”

Stability analysis and robust synchronisation of fractional-order modified Colpitts oscillators

“…So far, many types of chaos synchronisation have been proposed such as the phase synchronisation developed by Pecora and Carroll (2015). The complete synchronisation has also been developed by Liu et al (2002), adaptive synchronisation (Vaidyanathan et al, 2018b); anti-synchronisation (Vaidyanathan and Azar, 2015c). Added to these, there is also the projective synchronisation (Kammogne and Fotsin, 2014;Azar et al, 2018c), hybrid synchronisation (Yu et al, 2008;Ouannas et al, 2017g, 2017h;Vaidyanathan and Azar, 2015d), multi-switching synchronisation (Singh et al, , 2018a(Singh et al, , 2018b; Q-S synchronisation (Ouannas et al, 2017i), dead-beat synchronisation (Ouannas et al, 2017j).…”