scholarly journals Functional observers with linear error dynamics for nonlinear systems

2021 ◽  
Vol 157 ◽  
pp. 105021
Author(s):  
Costas Kravaris ◽  
Sunjeev Venkateswaran
Keyword(s):  
Nonlinear Systems ◽  
Error Dynamics

Disturbance Adaptive Discrete-Time Sliding Control With Application to Engine Speed Control

1998 ◽  
Vol 123 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Mooncheol Won ◽  
J. K. Hedrick
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Control Method ◽  
Sliding Mode ◽  
Input Saturation ◽  
Adaptive Sliding Mode Control ◽  
Control Law ◽  
Sliding Surface ◽  
Sliding Control ◽  
Error Dynamics

This paper presents a discrete-time adaptive sliding control method for SISO nonlinear systems with a bounded disturbance or unmodeled dynamics. Control and adaptation laws considering input saturation are obtained from approximately discretized nonlinear systems. The developed disturbance adaptation or estimation law is in a discrete-time form, and differs from that of conventional adaptive sliding mode control. The closed-loop poles of the feedback linearized sliding surface and the adaptation error dynamics can easily be placed. It can be shown that the adaptation error dynamics can be decoupled from sliding surface dynamics using the proposed scheme. The proposed control law is applied to speed tracking control of an automatic engine subject to unknown external loads. Simulation and experimental results verify the advantages of the proposed control law.

scholarly journals Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

Adaptive Robust Control for a Class of Non-Minimum Phase Nonlinear System

2006 ◽  
Author(s):  
Bo Xie ◽  
Bin Yao
Keyword(s):  
Robust Control ◽  
Nonlinear Systems ◽  
Tracking Error ◽  
Control Design ◽  
Adaptive Robust Control ◽  
Minimum Phase ◽  
Control Approach ◽  
Internal States ◽  
Robust Control Design ◽  
Error Dynamics

The paper presents the state feedback adaptive robust control approach to track the reference input for a class of nonminimum phase nonlinear systems. The key for this approach is to combine the adaptive robust control design techniques and the inputto-state property to deal with a class of non-minimum phase nonlinear systems with unknown parameter and unstructural uncertainties. The control design will guarantee that the tracking error dynamics is stabilized with bounded internal states and the closed-loop system is robust to the unstructural uncertainties.

scholarly journals Design of a Nonlinear Finite-Time Converging Observer for a Class of Nonlinear Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Frédéric Sauvage ◽  
Martin Guay ◽  
Denis Dochain
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Partial Derivative ◽  
Finite Time ◽  
Jacobian Matrix ◽  
The State ◽  
Two Systems ◽  
Error Dynamics

This paper proposes a nonlinear finite-time converging observer for a class of nonlinear systems. The estimate is recovered from the present and delayed estimates provided by two independent dynamical systems converging to a function of the state with linear error dynamics. The estimation is carried out using only the Jacobian matrix of both transformations determined by solving two systems of partial derivative equations. The results are illustrated on a bioreactor model.

A SYNCHRONIZATION CONDITION FOR COUPLED NONLINEAR SYSTEMS WITH TIME-DELAY: A FREQUENCY DOMAIN APPROACH

2011 ◽  
Vol 21 (09) ◽  
pp. 2525-2538 ◽  
Author(s):  
TOSHIKI OGUCHI ◽  
HENK NIJMEIJER
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Frequency Domain ◽  
Delay System ◽  
Coupled Systems ◽  
Feedback Connection ◽  
Circle Criterion ◽  
Synchronization Problem ◽  
Linear Delay ◽  
Error Dynamics

This paper considers the synchronization problem for nonlinear systems with time-delay couplings. We assume that the error dynamics can be rewritten as a feedback connection of a linear delay system with multiple inputs and outputs and nonlinear elements which are decentralized and satisfy a sector condition. Then, we derive a synchronization condition for time-delay coupled systems by applying the multivariable circle criterion. Unlike the conventional synchronization criteria, the derived criterion is based on a frequency-domain stability condition and avoids the use of the Lyapunov–Krasovskii approach. As a result, the condition based on the circle criterion does not contain the conservativeness caused by the Lyapunov–Krasovskii approach. The effectiveness of the proposed criterion is shown by examples of coupled Chua systems with delay coupling.

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