DISCRETE-TIME REDUCED ORDER NEURAL OBSERVERS FOR UNCERTAIN NONLINEAR SYSTEMS

2010 ◽  
Vol 20 (01) ◽  
pp. 29-38 ◽  
Author(s):  
ALMA Y. ALANIS ◽  
EDGAR N. SANCHEZ ◽  
LUIS J. RICALDE
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Nonlinear Oscillator ◽  
Estimation Error ◽  
Reduced Order ◽  
Lyapunov Approach ◽  
Simulation Results ◽  
Parallel Configuration ◽  
The Stability ◽  
High Order Neural Network

This paper focusses on a novel discrete-time reduced order neural observer for nonlinear systems, which model is assumed to be unknown. This neural observer is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter (EKF)-based algorithm, using a parallel configuration. This work includes the stability proof of the estimation error on the basis of the Lyapunov approach; to illustrate the applicability, simulation results for a nonlinear oscillator are included.

Full-Order and Reduced-Order Exponential Observers for Discrete-Time Nonlinear Systems With Incremental Quadratic Constraints

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Wei Zhang ◽  
Younan Zhao ◽  
Masoud Abbaszadeh ◽  
Mingming Ji
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Exponential Convergence ◽  
Estimation Error ◽  
Observer Design ◽  
Linear Matrix ◽  
Discrete Time System ◽  
Quadratic Constraints ◽  
Reduced Order ◽  
Reduced Order Observer

This paper considers the observer design problem for a class of discrete-time system whose nonlinear time-varying terms satisfy incremental quadratic constraints. We first construct a circle criterion based full-order observer by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the state estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is included to illustrate the effectiveness of the proposed design.

scholarly journals Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

2011 ◽  
Vol 62 (1) ◽  
pp. 44-48 ◽  
Author(s):  
Paknosh Karimaghaee ◽  
Navid Noroozi
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Linear Time ◽  
Order Reduction ◽  
Bilinear Transformation ◽  
Reduced Order ◽  
Linear Time Invariant ◽  
The Stability ◽  
Controllability And Observability ◽  
Time Invariant

Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear TransformationThis paper addresses a new method for order reduction of linear time invariant discrete-time controller. This method leads to a new algorithm for controller reduction when a discrete time controller is used to control a continuous time plant. In this algorithm, at first, a full order controller is designed ins-plane. Then, bilinear transformation is applied to map the closed loop system toz-plane. Next, new closed loop controllability and observability grammians are calculated inz-plane. Finally, balanced truncation idea is used to reduce the order of controller. The stability property of the reduced order controller is discussed. To verify the effectiveness of our method, a reduced controller is designed for four discs system.

scholarly journals Disturbance Attenuation and Rejection for a Class of Switched Nonlinear Systems Subject to Input and Sensor Saturations

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Yunliang Wei ◽  
Liping Sun ◽  
Shengsen Jia ◽  
Kunming Liu ◽  
Fanwei Meng
Keyword(s):  
Nonlinear Systems ◽  
Disturbance Attenuation ◽  
Switched Nonlinear Systems ◽  
Reduced Order ◽  
Closed Loop Systems ◽  
Augmented Systems ◽  
Bounded Disturbances ◽  
Effective Synthesis ◽  
System States ◽  
The Stability

This paper investigates the problem of disturbance attenuation and rejection for a class of switched nonlinear systems subject to input and sensor saturations, in which exosystem generated disturbances and H2-norm bounded disturbances are considered. The full-order and reduced-order observers are designed according to whether the system states are available or not. Based on the estimating values of the system states and exosystem generated disturbances, the design schemes for the composite controllers are put forward based on the full-order and reduced-order observers, respectively. For a switched system, the input and sensor saturations would influence the effective synthesis of observer and controller. By sector nonlinearity technology, the stability of the augmented closed-loop systems under the proposed composite controllers are analyzed, and the conditions of synthesis of the observers and controllers are further presented to ensure the augmented systems to be robustly asymptotically stable with a weighted H∞ performance level. An example is given to guarantee the effectiveness of the proposed control schemes.

scholarly journals Discrete-time sliding mode observer for the state estimation of a manoeuvring target

2019 ◽  
Vol 233 (7) ◽  
pp. 847-854
Author(s):  
K Harikumar ◽  
Titas Bera ◽  
Rajarshi Bardhan ◽  
Suresh Sundaram
Keyword(s):  
Boundary Layer ◽  
Discrete Time ◽  
Sliding Mode ◽  
Estimation Error ◽  
Sliding Mode Observer ◽  
Unknown Parameters ◽  
First Order ◽  
Error Dynamics ◽  
And Performance ◽  
The Stability

This article addresses the problem of estimating the position, velocity, and acceleration of a manoeuvring target from noisy position measurements. A discrete-time sliding mode observer is designed to handle unmeasured disturbance input and measurement noise. A first-order linear dynamics is considered for target acceleration. The acceleration input command and the pole of the first-order acceleration dynamics are considered to be unknown parameters with known upper bounds. A finite non-zero boundary layer is employed to reduce the chattering phenomenon typically associated with sliding mode observers. Analysis of estimation error dynamics is presented for the case where the discrete-time sliding mode observer is operating outside the boundary layer and also within the boundary layer. An algorithm is developed for obtaining the observer gain vector that guarantees the stability of the error dynamics. Numerical simulations and experimental results are presented to validate the stability and performance of the proposed observer.

scholarly journals State and Unknown Input Simultaneous Estimation for a Class of Discrete-Time Linear Implicit Models : A Heat Exchanger Pilot Process Application

2021 ◽  
Vol 297 ◽  
pp. 01011
Author(s):  
Karim Bouassem ◽  
El Mahfoud El Bouatmani ◽  
Abdellatif El Assoudi ◽  
El Hassane El Yaagoubi
Keyword(s):  
Heat Exchanger ◽  
Discrete Time ◽  
Estimation Error ◽  
Lyapunov Theory ◽  
Dynamic Equations ◽  
Linear Matrix ◽  
Simultaneous Estimation ◽  
Unknown Inputs ◽  
The Stability ◽  
Time Linear

In this paper, the design problem of simultaneous estimation of unmeasurable states and unknown inputs (UIs) is investigated for a class of discrete-time linear implicit models (DLIMs). The UIs affect both state and output of the system. The approach is based on the separation between dynamic and static relations in the considered DLDM. First, the method permitting to separate dynamic equations from static equations is exposed. Next, an augmented explicit model which contains the dynamic equations and the UIs is constructed. Then an unknown inputs observer (UIO) design in explicit structure is developed. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of linear matrix inequality (LMI). Finally, an illustrative application of a heat exchanger pilot process is given to show the good performances of the proposed method.

Event-triggered Neural Network-Based Adaptive Control for a Class of Uncertain Nonlinear Systems

2021 ◽  
pp. 2150275
Author(s):  
Hui Hu ◽  
Yang Li ◽  
Wei Yi ◽  
Yuebiao Wang ◽  
Fan Qu ◽  
...  
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Nonlinear Systems ◽  
Control Method ◽  
Uncertain Nonlinear Systems ◽  
Network Resource ◽  
Lyapunov Approach ◽  
Stability Method ◽  
The Stability ◽  
Event Triggered

In the paper, an event triggering adaptive control method based on neural network (NN) is proposed for a class of uncertain nonlinear systems with external disturbances. In order to reduce the network resource utilization, a novel event-triggered condition by the Lyapunov approach is proposed. In addition, the NN controller and adaptive parameters determined by the Lyapunov stability method are updated only at triggered instants to reduce the amount of calculation. Only one NN is used as the controller in the entire system. The stability analysis results of the closed-loop system are obtained by the Lyapunov approach, which shows that all the signals in the systems with bounded disturbance are semi-globally bounded. Zeno behavior is avoided. Finally, the analytical design is confirmed by the simulation results on a two-link robotic manipulator.

scholarly journals ON THE STABILIZATION OF PERIODIC ORBITS FOR DISCRETE TIME CHAOTIC SYSTEMS BY USING SCALAR FEEDBACK

2007 ◽  
Vol 17 (12) ◽  
pp. 4431-4442 ◽  
Author(s):  
ÖMER MORGÜL
Keyword(s):  
Periodic Orbits ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Delayed Feedback ◽  
Stabilization Problem ◽  
Unstable Periodic Orbits ◽  
Scalar Input ◽  
Simulation Results ◽  
The Stability ◽  
Stability Results

In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems by using a scalar input. We use a simple periodic delayed feedback law and present some stability results. These results show that all hyperbolic periodic orbits as well as some nonhyperbolic periodic orbits can be stabilized with the proposed method by using a scalar input, provided that some controllability or observability conditions are satisfied. The stability proofs also lead to the possible feedback gains which achieve stabilization. We will present some simulation results as well.

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