Comparative Controlling of the Lorenz Chaotic System Using the SMC and APP Methods

Abstract

The Lorenz chaotic system is based on a nonlinear behavior and this causes the system to be unstable. Therefore, two different controller models were developed and named as the adaptive pole placement and sliding mode control (SMC) methods for the establishment of continuous time nonlinear Lorenz chaotic system. In order to achieve this, an improved controller structure was developed first theoretically for both the controller methods and then tested practically using the numerical samples. During the establishment of adaptive pole placement method for the Lorenz chaotic system, various stages were applied. The nonlinear chaotic system was also linearized by means of Taylor Series expansion processes. In addition, the feedback matrix of the adaptive pole placement method was determined using linear Jacobian matrix. The chaotic system reached an equilibrium point by using both the SMC and adaptive pole placement methods; however the simulation results of the SMC had better success than adaptive pole placement control technique.

Optimizing FPGA implementation of high-precision chaotic systems for improved performance

“…The one-step numerical algorithms such as Euler, Heun, and Runge-Kutta (RK) methods, in addition to the multi-step algorithms, such as Adams-Bashforth and Adams-Moulton methods, are among the most famous choices, depending on the nature of the system, its stiffness, and whether it is integer or fractional order [ 19 ]. Microcontrollers, as a low-cost choice for implementing the discretized chaotic Lorenz system were explored in [ 20 ], where the Euler algorithm, with an integration step of 4.0 ms was used. An 8-bit PIC18F452 microcontroller was used, with a clock frequency of 10 MHz, while coding the algorithm using a CCS-C compiler.…”

Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

“…After that, the backstepping method has also been used for chaotic control of Lorenz system [21]. Kose and Mhrc have found that the SMC is superior to the adaptive pole placement control method for the Lorenz system [22]. For obtaining a fast convergence rate, the finite-time and fixed-time control techniques have been further implemented for chaotic Lorenz systems in recent years [23]- [25].…”

Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems

“…Chaos is an important phenomenon, which is famous for its sensitivity to initial conditions and parameter values. Apart from famous chaotic systems such as the weather forecast [5], finance [6] and biological [7] models, chaos in mechanical systems is demanding discussion in this technological era. In 2012, Aslanov and Yudintsev [8] considered a free gyrostat with small asymmetrical rotors and used an advanced Melinkov function to determine homoclinic and heteroclinic orbits in a controlled manner.…”