scholarly journals Nonlinear state-dependent feedback control of a pest-natural enemy system

2018 ◽  
Vol 94 (3) ◽  
pp. 2243-2263 ◽  
Author(s):  
Yuan Tian ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Feedback Control ◽  
Natural Enemy ◽  
State Dependent ◽  
Nonlinear State

scholarly journals Threshold Dynamics and Bifurcation of a State-Dependent Feedback Nonlinear Control Susceptible–Infected–Recovered Model1

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Tianyu Cheng ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Reproduction Number ◽  
Threshold Level ◽  
Sir Model ◽  
Threshold Dynamics ◽  
Threshold Condition ◽  
Susceptible Population ◽  
State Dependent ◽  
Nonlinear State

A classic susceptible–infected–recovered (SIR) model with nonlinear state-dependent feedback control is proposed and investigated in which integrated control measures, including vaccination, treatment and isolation, are applied once the number of the susceptible population reaches a threshold level. The interventions are density dependent due to limitations on the availability of resources. The existence and global stability of the disease-free periodic solution (DFPS) are addressed, and the threshold condition is provided, which can be used to define the control reproduction number Rc for the model with state-dependent feedback control. The DFPS may also be globally stable even if the basic reproduction number R0 of the SIR model is larger than one. To show that the threshold dynamics are determined by the Rc, we employ bifurcation theories of the discrete one-parameter family of maps, which are determined by the Poincaré map of the proposed model, and the main results indicate that under certain conditions, a stable or unstable interior periodic solution could be generated through transcritical, pitchfork, and backward bifurcations. A biphasic vaccination rate (or threshold level) could result in an inverted U-shape (or U-shape) curve, which reveals some important issues related to disease control and vaccine design in bioengineering including vaccine coverage, efficiency, and vaccine production. Moreover, the nonlinear state-dependent feedback control could result in novel dynamics including various bifurcations.

A state-dependent Riccati equation-based estimator approach for HIV feedback control

2006 ◽  
Vol 27 (2) ◽  
pp. 93-121 ◽  
Author(s):  
H. T. Banks ◽  
Hee-Dae Kwon ◽  
J. A. Toivanen ◽  
H. T. Tran
Keyword(s):  
Feedback Control ◽  
Riccati Equation ◽  
State Dependent

Nonlinear Robust H∞ Control With State-Dependent Scaling

2011 ◽  
Author(s):  
Scott Hays ◽  
Fen Wu
Keyword(s):  
Direct Method ◽  
State Feedback Control ◽  
Van Der Pol ◽  
Synthesis Conditions ◽  
State Dependent ◽  
Nonlinear Uncertain Systems ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties ◽  
Nonlinear State ◽  
Nonlinear Robust

This paper addresses the design of nonlinear robust H∞ controllers for nonlinear uncertain systems with polynomial vector field and norm bounded uncertainties. We derive state-dependent matrix inequalities, using Lyapunov’s direct method, that stabilize the nonlinear systems and guarantee robust performance using nonlinear state-feedback control. The state-dependent synthesis conditions incorporate state-dependent scaling to minimize the ℒ2 gain of the disturbance/output. Sum-of-squares (SOS) optimization is applied to solve the resulting synthesis condition with optimized ℒ2 gain for the nonlinear system, without requiring an iterative approach. Finally, a design example of nonlinear Van der Pol equation is presented.

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