Sliding Dynamics and Bifurcations in the Extended Nonsmooth Filippov Ecosystem

2021 ◽  
Vol 31 (08) ◽  
pp. 2150119
Author(s):  
Wenjie Qin ◽  
Xuewen Tan ◽  
Xiaotao Shi ◽  
Marco Tosato ◽  
Xinzhi Liu
Keyword(s):  
Sliding Mode ◽  
Threshold Value ◽  
Boundary Node ◽  
Refuge Strategy ◽  
Boundary Equilibrium ◽  
The Stability ◽  
Sliding Dynamics ◽  
Regular Equilibrium ◽  
Existence Of Equilibria ◽  
Sliding Mode Dynamics

We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular/virtual equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point. In particular, we consider how the existence of the regular equilibrium and the pseudo-equilibrium are related. Then we study the stability of the standard periodic solution (limit cycle), the sliding periodic solutions (grazing or touching cycle) and the dynamics of the pseudo equilibrium, using quantitative analysis techniques related to nonsmooth Filippov systems. Furthermore, as the threshold value is varied, the model exhibits several complex bifurcations which are classified into equilibria, sliding mode, local sliding (boundary node and focus) and global bifurcations (grazing or touching). In conclusion, we discuss the importance of the refuge strategy in a biological setting.

scholarly journals Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Xianghong Zhang ◽  
Sanyi Tang
Keyword(s):  
Sliding Mode ◽  
Threshold Level ◽  
Economic Threshold ◽  
Boundary Node ◽  
Threshold Policy ◽  
Ratio Dependent ◽  
Predator Model ◽  
The Stability ◽  
Globally Stable ◽  
Sliding Mode Dynamics

The Filippov ratio-dependent prey-predator model with economic threshold is proposed and studied. In particular, the sliding mode domain, sliding mode dynamics, and the existence of four types of equilibria and tangent points are investigated firstly. Further, the stability of pseudoequilibrium is addressed by using theoretical and numerical methods, and also the local sliding bifurcations including regular/virtual equilibrium bifurcations and boundary node bifurcations are studied. Finally, some global sliding bifurcations are addressed numerically. The globally stable touching cycle indicates that the density of pest population can be successfully maintained below the economic threshold level by designing suitable threshold policy strategies.

Another Note on Stability of Sliding Mode Dynamics in Suppression of Fractional Chaotic Systems

2015 ◽  
Vol 743 ◽  
pp. 303-306
Author(s):  
J. Yuan ◽  
B. Shi ◽  
Yan Wang
Keyword(s):  
Stability Analysis ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Fractional Systems ◽  
Infinite Dimensional ◽  
Fractional Integrator ◽  
Fractional Differential ◽  
Continuous Frequency ◽  
The Stability ◽  
Sliding Mode Dynamics

This paper revisits the stability analysis of sliding mode dynamics in suppression of a classof fractional chaotic systems by a different approach. Firstly, we convert fractional differential equationsinto infinite dimensional ordinary differential equations based on the continuous frequency distributedmodel of the fractional integrator. Then we choose a Lyapunov function candidate to proposethe stability analysis. The result applies to both the commensurate fractional systems and the incommensurateones.

scholarly journals Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Yuan ◽  
Bao Shi ◽  
Zhentao Yu
Keyword(s):  
Chaotic Systems ◽  
Sliding Mode ◽  
Adaptive Sliding Mode Control ◽  
External Disturbances ◽  
Fractional Systems ◽  
Sliding Control ◽  
Sliding Manifold ◽  
The Stability ◽  
Adaptation Law ◽  
Sliding Dynamics

This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems. We firstly introduce a fractional integral sliding manifold for the nominal systems. Secondly we prove the stability of the corresponding fractional sliding dynamics. Then, by introducing a Lyapunov candidate function and using the Mittag-Leffler stability theory we derive the desired sliding control law. Furthermore, we prove that the proposed sliding manifold is also adapted for the fractional systems in the presence of uncertainties and external disturbances. At last, we design a fractional adaptation law for the perturbed fractional systems. To verify the viability and efficiency of the proposed fractional controllers, numerical simulations of fractional Lorenz’s system and Chen’s system are presented.

SLIDING BIFURCATION AND GLOBAL DYNAMICS OF A FILIPPOV EPIDEMIC MODEL WITH VACCINATION

2013 ◽  
Vol 23 (08) ◽  
pp. 1350144 ◽  
Author(s):  
AILI WANG ◽  
YANNI XIAO
Keyword(s):  
Epidemic Model ◽  
Sliding Mode ◽  
Vaccination Strategy ◽  
Threshold Value ◽  
Threshold Level ◽  
Vaccination Rate ◽  
Global Dynamics ◽  
Boundary Node ◽  
Threshold Policy ◽  
Sliding Bifurcation

This paper proposes a Filippov epidemic model with piecewise continuous function to represent the enhanced vaccination strategy being triggered once the proportion of the susceptible individuals exceeds a threshold level. The sliding bifurcation and global dynamics for the proposed system are investigated. It is shown that as the threshold value varies, the proposed system can exhibit variable sliding mode domains and local sliding bifurcations including boundary node (focus) bifurcation, double tangency bifurcation and other sliding mode bifurcations. Model solutions ultimately approach either one of two endemic states for two structures or the pseudo-equilibrium on the switching surface, depending on the threshold level. The findings indicate that proper combinations of threshold level and enhanced vaccination rate based on threshold policy can lead disease prevalence to a previously chosen level if eradication of disease is impossible.

Control of Bidirectional AC-DC Converters for DC Microgrid Application

2014 ◽  
Vol 536-537 ◽  
pp. 1219-1222
Author(s):  
Yuan Sheng Xiong ◽  
Shang Xing Ma
Keyword(s):  
Sliding Mode ◽  
Reference Value ◽  
Threshold Value ◽  
Pi Controller ◽  
Dc Microgrid ◽  
Current Reference ◽  
Dc Bus ◽  
Bus Voltage ◽  
Grid Connected Inverter ◽  
The Stability

Three-phase bidirectional AC/DC converter acts as a key part in DC microgrid. To improve the stability of DC bus voltage for the grid-connected mode in DC microgrid, a sliding mode or PI controller based on SVPWM modulator is designed for the bidirectional AC/DC converter in inverter mode. When the error between grid-connected current reference value and actual value is larger than the threshold value, the sliding mode controller is used. Otherwise, the PI controller is adopted. The great grid-connected current reference value fluctuation is simulated in PSIM software when the DC microgrid operates in the grid-connected inverter mode. The simulation results show that the gird-connected current actual value can fast track with the reference value. Then the dynamic response performance of DC bus voltage is improved.

scholarly journals Delay compensation based controller for rotary electrohydraulic servo system

2021 ◽  
Author(s):  
Zakarya Omar ◽  
Xingsong Wang ◽  
Khalid Hussain ◽  
Mingxing Yang
Keyword(s):  
High Frequency ◽  
Dead Time ◽  
Sliding Mode ◽  
Servo System ◽  
Smith Predictor ◽  
Delay Compensation ◽  
Mechanical Parts ◽  
System Output ◽  
Electrohydraulic Servo System ◽  
The Stability

AbstractThe typical power-assisted hip exoskeleton utilizes rotary electrohydraulic actuator to carry out strength augmentation required by many tasks such as running, lifting loads and climbing up. Nevertheless, it is difficult to precisely control it due to the inherent nonlinearity and the large dead time occurring in the output. The presence of large dead time fires undesired fluctuation in the system output. Furthermore, the risk of damaging the mechanical parts of the actuator increases as these high-frequency underdamped oscillations surpass the natural frequency of the system. In addition, system closed-loop performance is degraded and the stability of the system is unenviably affected. In this work, a Sliding Mode Controller enhanced by a Smith predictor (SMC-SP) scheme that counts for the output delay and the inherent parameter nonlinearities is presented. SMC is utilized for its robustness against the uncertainty and nonlinearity of the servo system parameters whereas the Smith predictor alleviates the dead time of the system’s states. Experimental results show smoother response of the proposed scheme regardless of the amount of the existing dead time. The response trajectories of the proposed SMC-SP versus other control methods were compared for a different predefined dead time.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

scholarly journals Sliding Mode Control and Geometrization Conjecture in Seismic Response

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 353
Author(s):  
Ligia Munteanu ◽  
Dan Dumitriu ◽  
Cornel Brisan ◽  
Mircea Bara ◽  
Veturia Chiroiu ◽  
...  
Keyword(s):  
Sliding Mode Control ◽  
Ricci Flow ◽  
Lyapunov Functions ◽  
Seismic Waves ◽  
Sliding Mode ◽  
Flow Process ◽  
Mode Control ◽  
Finite Period ◽  
The Stability ◽  
Story Building

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov functions, the first associated with slipping in a finite period of time and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to minimization of the displacements of the floors.

scholarly journals Stability Control for Electric Vehicles with Four In-Wheel-Motors Based on Sideslip Angle

2021 ◽  
Vol 12 (1) ◽  
pp. 42
Author(s):  
Kun Yang ◽  
Danxiu Dong ◽  
Chao Ma ◽  
Zhaoxian Tian ◽  
Yile Chang ◽  
...  
Keyword(s):  
Electric Vehicles ◽  
Control Method ◽  
Sliding Mode ◽  
Stability Control ◽  
Torque Control ◽  
Wheel Load ◽  
Sideslip Angle ◽  
Distribution Method ◽  
Load Rate ◽  
The Stability

Tire longitudinal forces of electrics vehicle with four in-wheel-motors can be adjusted independently. This provides advantages for its stability control. In this paper, an electric vehicle with four in-wheel-motors is taken as the research object. Considering key factors such as vehicle velocity and road adhesion coefficient, the criterion of vehicle stability is studied, based on phase plane of sideslip angle and sideslip-angle rate. To solve the problem that the sideslip angle of vehicles is difficult to measure, an algorithm for estimating the sideslip angle based on extended Kalman filter is designed. The control method for vehicle yaw moment based on sliding-mode control and the distribution method for wheel driving/braking torque are proposed. The distribution method takes the minimum sum of the square for wheel load rate as the optimization objective. Based on Matlab/Simulink and Carsim, a cosimulation model for the stability control of electric vehicles with four in-wheel-motors is built. The accuracy of the proposed stability criterion, the algorithm for estimating the sideslip angle and the wheel torque control method are verified. The relevant research can provide some reference for the development of the stability control for electric vehicles with four in-wheel-motors.

A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads

2021 ◽  
pp. 095441002110136
Author(s):  
Nasim Ullah ◽  
Irfan Sami ◽  
Wang Shaoping ◽  
Hamid Mukhtar ◽  
Xingjian Wang ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Computationally Efficient ◽  
Control Scheme ◽  
Control Schemes ◽  
Adaptive Laws ◽  
Unknown Disturbances ◽  
The Stability

This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.

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