Adaptive Controller and Observer Design for a Class of Nonlinear Systems

2005 ◽  
Vol 128 (3) ◽  
pp. 712-717 ◽  
Author(s):  
Yongliang Zhu ◽  
Prabhakar R. Pagilla
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Adaptive Controller ◽  
Observer Design ◽  
Dynamic Friction ◽  
Unknown Parameters ◽  
Single Link ◽  
Suitable Form ◽  
Parameter Dependent

Design of a stable adaptive controller and observer for a class of nonlinear systems that contain product of unmeasurable states and unknown parameters is considered. The nonlinear system is cast into a suitable form based on which a stable adaptive controller and observer are designed using a parameter dependent Lyapunov function. The class of nonlinear systems considered is practically relevant; mechanical systems with dynamic friction fall into this category. Experimental results on a single-link mechanical system with dynamic friction are shown for the proposed design.

Design of Globally Adaptive Stabilizer for Underwater Navigator

2010 ◽  
Vol 108-111 ◽  
pp. 1119-1123
Author(s):  
Yi Mei Chen
Keyword(s):  
Vector Field ◽  
Lyapunov Function ◽  
Function Method ◽  
Adaptive Controller ◽  
Adaptive Stabilization ◽  
Unknown Parameters ◽  
Control Lyapunov Function ◽  
Lyapunov Function Method ◽  
Projection Techniques ◽  
Adaptive Stabilizer

In this paper, the problem of adaptive stabilization of an underwater navigator with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method and parameter projection techniques, a direct adaptive controller is designed to complete the globally adaptive stability of the navigator. Simulations are provided to illustrate the effectiveness of our proposed method.

ADAPTIVE OBSERVER-BASED SYNCHRONIZATION FOR COMMUNICATION

2000 ◽  
Vol 10 (12) ◽  
pp. 2807-2813 ◽  
Author(s):  
ALEXANDER FRADKOV ◽  
HENK NIJMEIJER ◽  
ALEXEY MARKOV
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Signal Transmission ◽  
Adaptive Observer ◽  
Simple Design ◽  
Quadratic Lyapunov Function ◽  
Unknown Parameters ◽  
Error System

The problem of synchronizing two nonlinear systems (transmitter and receiver) is considered. A simple design of an adaptive observer for estimating the unknown parameters of the transmitter is proposed based on the design of quadratic Lyapunov function for the error system. The results are illustrated by an example of signal transmission based on a pair of synchronizing Chua circuits.

scholarly journals Dynamic Neural Network Identification and Decoupling Control Approach for MIMO Time-Varying Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhixi Shen ◽  
Kai Zhao
Keyword(s):  
Neural Network ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Time Varying ◽  
Dynamic Neural Networks ◽  
Control Approach ◽  
The Neural Network ◽  
And Control

Overcoming the coupling among variables is greatly necessary to obtain accurate, rapid and independent control of the real nonlinear systems. In this paper, the main methodology, on which the method is based, is dynamic neural networks (DNN) and adaptive control with the Lyapunov methodology for the time-varying, coupling, uncertain, and nonlinear system. Under the framework, the DNN is developed to accommodate the identification, and the weights of DNN are iteratively and adaptively updated through the identification errors. Based on the neural network identifier, the adaptive controller of complex system is designed in the latter. To guarantee the precision and generality of decoupling tracking performance, Lyapunov stability theory is applied to prove the error between the reference inputs and the outputs of unknown nonlinear system which is uniformly ultimately bounded (UUB). The simulation results verify that the proposed identification and control strategy can achieve favorable control performance.

scholarly journals Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Sohaira Ahmad ◽  
Raafia Majeed ◽  
Keum-Shik Hong ◽  
Muhammad Rehan
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Time Lag ◽  
Time Derivative ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Lipschitz Nonlinear Systems ◽  
System States ◽  
Lipschitz Systems

This paper presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systems in the presence of output delays. The crux of the approach is to overcome the practical consequences of time delays, encountered due to distant sensor position and time lag in measurement, for estimation of physical and engineering nonlinear system states. A Lyapunov-Krasovskii functional is employed, the time derivative of which is solved using Jensen’s inequality, one-sided Lipschitz condition, and quadratic inner-boundedness, and, accordingly, design conditions for delay-range-dependent nonlinear observer for delayed one-sided Lipschitz systems are derived. Further, novel solutions to the problems of delay-dependent observer synthesis of one-sided Lipschitz models and delay-range-dependent state estimation of linear and Lipschitz nonlinear systems are deduced from the present delay-range-dependent technique. An observer formulation methodology for retrieval of one-sided Lipschitz nonlinear-system states, which is robust againstL2norm-bounded perturbations, is devised. The resultant design conditions, in contrast to the conventional procedures, can be solved via less conservative linear matrix inequality- (LMI-) based routines that succeed by virtue of additional LMI variables, meaningful transformations, and cone complementary linearization algorithm. Numerical examples are worked out to illustrate the effectiveness of the proposed observer-synthesis approach for delayed one-sided Lipschitz systems.

Observer-Based State Tracking Adaptive Controller for a Class of Non-Affine Nonlinear Systems: An Intelligent Approach

2012 ◽  
Vol 488-489 ◽  
pp. 1798-1802
Author(s):  
R. Ghasemi ◽  
M.B. Menhaj ◽  
B. Abdi
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Tracking Error ◽  
Adaptive Controller ◽  
Nonlinear Observer ◽  
Asymptotic Convergence ◽  
Affine Nonlinear Systems ◽  
State Tracking ◽  
Simulation Results ◽  
Intelligent Approach

This paper proposes a new method for designing both nonlinear observer and adaptive controller for a class of non-affine nonlinear systems with unknown functions of the system. The states of the nonlinear system are assumed to be unavailable for measurement. The merits of this paper is as: asymptotic convergence of the observer and tracking error to zero, boundedness of all signals involved, and robustness. The simulation results illustrate the promising performance of the proposed algorithm.

Analysis of Sliding Mode Observers for Nonlinear Systems Using a Time-Averaged Lyapunov Function

2018 ◽  
Author(s):  
Sagar Mehta ◽  
Krishna Vijayaraghavan
Keyword(s):  
Steady State ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Convergence Rate ◽  
Sliding Mode ◽  
Sliding Mode Observer ◽  
Sensor Noise ◽  
Sliding Mode Observers

This paper is an extension of the authors’ previous paper on the analysis of sliding mode observers using a novel Time-Averaged Lyapunov function [1]. The paper presents the design of a sliding mode observer for a Lipschitz nonlinear system. The paper demonstrates that the external sensor noise (Gaussian) only affects the convergence rate of the observer without having any influence over its stability at steady state. Further, a condition for the existence of the observer is provided in the form of an LMI. The LMI can be solved offline using various commercial LMI solvers. An illustrative example is presented to demonstrate the effectiveness of this approach.

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