scholarly journals Bounded finite-time stabilization of the prey – predator model via Korobov’s controllability function

2021 ◽  
Vol 21 (1) ◽  
pp. 76-87
Author(s):  
Abdon E. Choque-Rivero ◽  
◽  
Fernando Ornelas-Tellez ◽  
Keyword(s):  
Equilibrium Point ◽  
Finite Time ◽  
Control Input ◽  
Bounded Control ◽  
Physical Restriction ◽  
Simulation Results ◽  
Finite Time Stabilization ◽  
Predator Model ◽  
Control Methodology ◽  
Predator System

The problem of finite-time stabilization for a Leslie-Gower prey – predator system through a bounded control input is solved. We use Korobov’s controllability function. The trajectory of the resulting motion is ensured for fulfilling a physical restriction that prey and predator cannot achieve negative values. For this purpose, a certain ellipse depending on given data and the equilibrium point of the considered system is constructed. Simulation results show the effectiveness of the proposed control methodology.

scholarly journals Global Finite-Time Stabilization Problem of Affine Nonlinear Systems with Unknown Functions

2021 ◽  
Author(s):  
Fujin Jia ◽  
Junwei Lu ◽  
Yong-Min Li ◽  
Fangyuan Li
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Control Algorithm ◽  
Lyapunov Analysis ◽  
Stabilization Problem ◽  
Analysis Method ◽  
Control Approach ◽  
Affine Nonlinear Systems ◽  
Simulation Results ◽  
Finite Time Stabilization

In this paper, the global finite-time stabilization (FTS) of nonlinear systems with unknown functions (UFs) is studied. Firstly, in order to deal with UFs, a Lemma is proposed to avoid the Assumptions of UFs. Secondly, based on this Lemma, the control algorithm designed by using backstepping has no partial derivative of virtual controllers, so it avoids the “differential explosion” problem of backstepping. Thirdly, by using Lyapunov analysis method, backstepping and FTS method, a global FTS control algorithm of nonlinear systems with UFs is proposed. Finally, the feasibility of developed control approach is illustrated by the simulation results of a manipulator.

scholarly journals Finite Time Stability of Finance Systems with or without Market Confidence Using Less Control Input

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Ma ◽  
Yujuan Tian ◽  
Zhongfeng Qu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Input ◽  
Three Dimension ◽  
Time Stability ◽  
Finance System ◽  
Finite Time Stability ◽  
Single Controller ◽  
Simulation Results

In this paper, we make an exploration of a technique to control a class of finance chaotic systems. This technique allows one to achieve the finite time stability of the finance system more effectively with less control input energy. First, the finite time stability of three dimension finance system without market confidence is analyzed by using a single controller. Then, two controllers are designed to stabilize the four-dimension finance system with market confidence. Moreover, the finite time stability of the three-dimension and four-dimension finance system with unknown parameter is also studied. Finally, simulation results are presented to show the chaotic behaviour of the finance systems, verify the effectiveness of the proposed control method, and illustrate its advantages compared with other methods.

scholarly journals Korobov's controllability function method applied to finite-time stabilization of the Rössler system via bounded controls

2020 ◽  
Keyword(s):  
Equilibrium Point ◽  
Finite Time ◽  
Function Method ◽  
Equilibrium Points ◽  
Synthesis Problem ◽  
Bounded Controls ◽  
Rossler System ◽  
Rössler System ◽  
Finite Time Stabilization ◽  
Controllability Function Method

Rössler system has become one of the reference chaotic systems. Its novelty when introduced, being that exhibits a chaotic attractor generated by a simpler set of nonlinear differential equations than Lorenz system. It develops chaotic behaviour for certain values of its parameter triplet. The issue of controlling Rössler system by stabilizing one of its unstable equilibrium points has been previously dealt with in the literature. In this work, control of the Rössler system is stated by considering the synthesis problem. Given a system and one of its equilibrium points, the synthesis problem consists in constructing a bounded positional control such that for any x⁰ belonging to a certain neighborhood of the equilibrium point, the trajectory x(t) initiated in x⁰ arrives at this equilibrium point in finite time. Namely, by using V. I. Korobov’s method, also called the controllability function method, a family of bounded positional controls that solve the synthesis problem for the Rössler system is proposed. We mainly use two ingredients. The first one concerns the general theory of the controllability function The second ingredient is a family of bounded positional controls that was obtained in. Different from previous works on finite-time stabilization we propose an explicit family of bounded controls constructed by taking into account the only nonlinearity of the Rössler system, which is a quadratic function. By using the controllability function method, which is a Lyapunov-type function, the finite time to reach the desired equilibrium point is estimated. This is obtained for an arbitrary given control bound and an adequate set of initial conditions to achieve the control objective is computed. This proposal may also be developed for any controlled system for which its linear part is completely controllable and its corresponding nonlinear part is a lipschitzian function in a neighborhood of the equilibrium point. In turn, this technique may be implemented as a tool for control chaos.

scholarly journals A New Finite-Time Bounded Control of Stochastic Itô Systems with (x,u,v)-Dependent Noise: Different Quadratic Function Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Zhiguo Yan ◽  
Zhongwei Lin
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Quadratic Function ◽  
Function Approach ◽  
Control Input ◽  
Matrix Inequalities ◽  
Bounded Control ◽  
Linear Stochastic Systems ◽  
Nonlinear Matrix ◽  
Finite Time Boundedness

This paper addresses the finite-time bounded control problem of linear stochastic systems with state, control input, and external disturbance-dependent noise ((x,u,v)-dependent noise for short). The notion of finite-time boundedness of linear stochastic systems is first introduced. Then a different quadratic function approach is proposed to give a sufficient condition for finite-time boundedness of such a class of systems, and its superiority to common quadratic approach is shown. Moreover, the finite-time bounded controller design problem is studied and two sufficient conditions for the existence of state and output feedback controllers are presented in terms of nonlinear matrix inequalities. An algorithm is given for solving the obtained nonlinear matrix inequalities. Finally, an example is employed to illustrate the effectiveness of our obtained results.

Stabilization of nonlinear vibrations of carbon nanotubes using observer-based terminal sliding mode control

2019 ◽  
Vol 42 (5) ◽  
pp. 1047-1058 ◽  
Author(s):  
Amin Yousefpour ◽  
Amin Vahidi-Moghaddam ◽  
Arman Rajaei ◽  
Moosa Ayati
Keyword(s):  
Carbon Nanotube ◽  
Finite Time ◽  
Disturbance Observer ◽  
Sliding Mode ◽  
Nonlinear Partial Differential Equation ◽  
Sliding Mode Controller ◽  
Control Input ◽  
Control Force ◽  
Terminal Sliding Mode ◽  
Simulation Results

This article is concerned with suppression of nonlinear forced vibration of a single-wall carbon nanotube conveying fluid based on the nonlocal elasticity theory and Euler–Bernoulli beam theory. Electrostatic actuation is considered as the control force for the suppression of carbon nanotube. Based on Galerkin approach, the governing nonlinear partial differential equation is reduced to an ordinary one. Since the sliding mode controller (SMC) does not assures finite time system stabilization and also causes chattering in the control input and consequently vibration in the system, terminal sliding mode controller (TSMC) is developed for the stabilization of carbon nanotube based on a disturbance observer. TSMC and disturbance observer suppress the vibrations of nanotube in the presence of external disturbances caused by the internal flow. Numerical simulation results are presented to illustrate the effectiveness and performance of the proposed control scheme in comparison to similar approaches. Simulation results show that the proposed control method successfully stabilizes the uncertain system in a finite time.

scholarly journals Stability Analysis of Prey-Predator Model With Holling Type IV Functional Response and Infectious Predator

2020 ◽  
Vol 17 (2) ◽  
pp. 155-165
Author(s):  
A. Muh. Amil Siddik ◽  
Syamsuddin Toaha ◽  
Andi Muhammad Anwar
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Functional Response ◽  
Local Stability ◽  
Jacobian Matrix ◽  
Equilibrium Points ◽  
Type Iv ◽  
Simulation Results ◽  
Predator Model ◽  
Parameter Values

Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except , that may exist and stable. Simulation results show that with the variation of several parameter values infection rate of disease , the diseases in the system may become endemic, or may become free from endemic.  

scholarly journals An Eco-Epidemiological Model Incorporating Harvesting Factors

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2179
Author(s):  
Kawa Hassan ◽  
Arkan Mustafa ◽  
Mudhafar Hama
Keyword(s):  
Equilibrium Point ◽  
Functional Response ◽  
Biological System ◽  
Numerical Verification ◽  
Interior Equilibrium ◽  
Dynamical Fluctuations ◽  
Predator Model ◽  
The Stability ◽  
Analytical Section ◽  
Predator System

The biological system relies heavily on the interaction between prey and predator. Infections may spread from prey to predators or vice versa. This study proposes a virus-controlled prey-predator system with a Crowley–Martin functional response in the prey and an SI-type in the prey. A prey-predator model in which the predator uses both susceptible and sick prey is used to investigate the influence of harvesting parameters on the formation of dynamical fluctuations and stability at the interior equilibrium point. In the analytical section, we outlined the current circumstances for all possible equilibria. The stability of the system has also been explored, and the required conditions for the model’s stability at the equilibrium point have been found. In addition, we give numerical verification for our analytical findings with the help of graphical illustrations.

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