scholarly journals Robust Synchronization of Delayed Chaotic FitzHugh-Nagumo Neurons under External Electrical Stimulation

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Rehan ◽  
Keum-Shik Hong
Keyword(s):  
Electrical Stimulation ◽  
Nonlinear Control ◽  
Control Law ◽  
Input Control ◽  
Control Schemes ◽  
Multiple Input ◽  
Cognitive Diseases ◽  
Single Input ◽  
Error Dynamics ◽  
Nonlinear Control Law

Synchronization of chaotic neurons under external electrical stimulation (EES) is studied in order to understand information processing in the brain and to improve the methodologies employed in the treatment of cognitive diseases. This paper investigates the dynamics of uncertain coupled chaotic delayed FitzHugh-Nagumo (FHN) neurons under EES for incorporated parametric variations. A global nonlinear control law for synchronization of delayed neurons with known parameters is developed. Based on local and global Lipschitz conditions, knowledge of the bounds on the neuronal states, the Lyapunov-Krasovskii functional, and theL2gain reduction, a less conservative local robust nonlinear control law is formulated to address the problem of robust asymptotic synchronization of delayed FHN neurons under parametric uncertainties. The proposed local control law guarantees both robust stability and robust performance and provides theL2bound for uncertainty rejection in the synchronization error dynamics. Separate conditions for single-input and multiple-input control schemes for synchronization of a wide class of FHN systems are provided. The results of the proposed techniques are verified through numerical simulations.

Analysis of a Nonlinear Control Law with Cubic Nonlinearity

2021 ◽  
Author(s):  
Melnikov Vitaly ◽  
Melnikov Gennady ◽  
Dudarenko Natalia
Keyword(s):  
Nonlinear Control ◽  
Control Law ◽  
Cubic Nonlinearity ◽  
Nonlinear Control Law

Nonlinear control law for aerial towed target

1995 ◽  
Vol 18 (6) ◽  
pp. 1232-1238 ◽  
Author(s):  
Alexander S. Bourmistrov ◽  
Robin D. Hill ◽  
Paul Riseborough
Keyword(s):  
Nonlinear Control ◽  
Control Law ◽  
Nonlinear Control Law

scholarly journals Synthetic Jet Actuator-Based Aircraft Tracking Using a Continuous Robust Nonlinear Control Strategy

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
N. Ramos-Pedroza ◽  
W. MacKunis ◽  
M. Reyhanoglu
Keyword(s):  
Nonlinear Control ◽  
Trajectory Tracking ◽  
Parameter Uncertainty ◽  
Tracking Error ◽  
Synthetic Jet ◽  
Parameter Estimates ◽  
Control Law ◽  
Robust Nonlinear Control ◽  
Trajectory Tracking Control ◽  
Nonlinear Control Law

A robust nonlinear control law that achieves trajectory tracking control for unmanned aerial vehicles (UAVs) equipped with synthetic jet actuators (SJAs) is presented in this paper. A key challenge in the control design is that the dynamic characteristics of SJAs are nonlinear and contain parametric uncertainty. The challenge resulting from the uncertain SJA actuator parameters is mitigated via innovative algebraic manipulation in the tracking error system derivation along with a robust nonlinear control law employing constant SJA parameter estimates. A key contribution of the paper is a rigorous analysis of the range of SJA actuator parameter uncertainty within which asymptotic UAV trajectory tracking can be achieved. A rigorous stability analysis is carried out to prove semiglobal asymptotic trajectory tracking. Detailed simulation results are included to illustrate the effectiveness of the proposed control law in the presence of wind gusts and varying levels of SJA actuator parameter uncertainty.

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