Upper Bounds for Induced Operator Norms of Nonlinear Systems

2007 ◽  
Author(s):  
Vahid Zahedzadeh ◽  
Horacio J. Marquez ◽  
Tongwen Chen
Keyword(s):  
Nonlinear Systems ◽  
Upper Bounds ◽  
Operator Norms ◽  
Induced Operator

Upper Bounds for Induced Operator Norms of Nonlinear Systems

2009 ◽  
Vol 54 (5) ◽  
pp. 1159-1165 ◽  
Author(s):  
V. Zahedzadeh ◽  
H.J. Marquez ◽  
Tongwen Chen
Keyword(s):  
Nonlinear Systems ◽  
Upper Bounds ◽  
Operator Norms ◽  
Induced Operator

scholarly journals Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1242
Author(s):  
Cong Huang ◽  
Bo Shen ◽  
Lei Zou ◽  
Yuxuan Shen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Estimation Error ◽  
Upper Bounds ◽  
The State ◽  
Fault Estimation ◽  
Triggering Mechanism ◽  
Transmission Frequency ◽  
Current Transmission ◽  
Event Triggering

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

scholarly journals A New Finite-Time Observer for Nonlinear Systems: Applications to Synchronization of Lorenz-Like Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Ricardo Aguilar-López ◽  
Juan L. Mata-Machuca
Keyword(s):  
Nonlinear Systems ◽  
Control Theory ◽  
Finite Time ◽  
Numerical Experiments ◽  
Time Synchronization ◽  
Upper Bounds ◽  
Observer Design ◽  
Synchronization Error ◽  
Chaotic Oscillator ◽  
Chaotic Oscillators

This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme.

Robust sliding model control-based adaptive tracker for a class of nonlinear systems with input nonlinearities and uncertainties

2020 ◽  
pp. 014233122097611
Author(s):  
Jiunn-Shiou Fang ◽  
Jason Sheng-Hong Tsai ◽  
Jun-Juh Yan ◽  
Shu-Mei Guo
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Controlled System ◽  
Control Laws ◽  
Model Control ◽  
Simulation Results ◽  
Robust Adaptive

A robust adaptive tracker is newly proposed for a class of nonlinear systems with input nonlinearities and uncertainties. Because the upper bounds of input nonlinearities and uncertainties are difficult to be acquired, the adaptive control integrated with sliding mode control (SMC) and radial basis function neural network (RBFNN) are utilized to cope with these undesired problems and effectively complete the robust tracker design. The main contributions are concluded as follows: (1) new sufficient conditions are obtained such that the proposed adaptive control laws can avoid overestimation; (2) A smooth [Formula: see text] function is introduced to eliminate the undesired chattering phenomenon in the traditional SMC systems; (3) A robust tracker is proposed such that the controlled system outputs can robustly track the pre-specified trajectories directly, even when subjected to unknown input nonlinearities and uncertainties. Finally, the numerical simulation results are illustrated to verify the proposed approach.

scholarly journals Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Raheleh Jafari ◽  
Wen Yu
Keyword(s):  
Nonlinear Systems ◽  
Set Theory ◽  
Nonlinear Modeling ◽  
Upper Bounds ◽  
Equation Model ◽  
Uncertain Nonlinear Systems ◽  
Modeling Process ◽  
Modeling Errors ◽  
The Neural Networks ◽  
Fuzzy Equations

The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.

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