Nonlinear Observers with Linearizable Error Dynamics

1985 ◽  
Vol 23 (2) ◽  
pp. 197-216 ◽  
Author(s):  
Arthur J. Krener ◽  
Witold Respondek
Keyword(s):  
Nonlinear Observers ◽  
Error Dynamics

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.

Feedback control framework for car-like robots using the unicycle controllers

Robotica ◽  
2011 ◽  
Vol 30 (4) ◽  
pp. 517-535 ◽  
Author(s):  
Maciej Michałek ◽  
Krzysztof Kozłowski
Keyword(s):  
Stability Analysis ◽  
Feedback Control ◽  
Closed Loop ◽  
Path Following ◽  
Rear Wheel ◽  
Front Wheel ◽  
Steering Angle ◽  
Formal Stability ◽  
Control Framework ◽  
Error Dynamics

SUMMARYThe paper introduces a novel general feedback control framework, which allows applying the motion controllers originally dedicated for the unicycle model to the motion task realization for the car-like kinematics. The concept is formulated for two practically meaningful motorizations: with a front-wheel driven and with a rear-wheel driven. All the three possible steering angle domains for car-like robots—limited and unlimited ones—are treated. Description of the method is complemented by the formal stability analysis of the closed-loop error dynamics. The effectiveness of the method and its limitations have been illustrated by numerous simulations conducted for the three main control tasks, namely, for trajectory tracking, path following, and set-point regulation.

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