Stochastically Resilient Observer Design for a Class of Discrete-Time Nonlinear Systems

2011 ◽  
Author(s):  
Chung Seop Jeong ◽  
Edwin E. Yaz ◽  
Yvonne I. Yaz
Keyword(s):  
Discrete Time ◽  
Estimation Error ◽  
Finite Energy ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Computational Errors ◽  
Simple Estimation ◽  
Measurement Equations

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based nonlinear observer design approach is presented, which guarantees the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of random perturbations, due possibly to computational errors or changes during operation, on the observer gain. Some simulation examples are included to illustrate the proposed design methodology.

scholarly journals Observer Design for Simultaneous State and Fault Estimation for a Class of Discrete-time Descriptor Linear Models

2021 ◽  
Vol 229 ◽  
pp. 01020
Author(s):  
Kaoutar Ouarid ◽  
Abdellatif El Assoudi ◽  
Jalal Soulami ◽  
El Hassane El Yaagoubi
Keyword(s):  
Discrete Time ◽  
Linear Models ◽  
Estimation Error ◽  
Equivalent Form ◽  
Observer Design ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Actuator Faults ◽  
Algebraic Equations

This paper investigates the problem of observer design for simultaneous states and faults estimation for a class of discrete-time descriptor linear models in presence of actuator and sensor faults. The idea of the present result is based on the second equivalent form of implicit model [1] which permits to separate the differential and algebraic equations in the considered singular model, and the use of an explicit augmented model structure. At that stage, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. Next, the explicit structure of the augmented model is established. Then, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. By using the Lyapunov approach, the convergence of the state estimation error of the augmented system is analyzed, and the observer’s gain matrix is achieved by solving only one linear matrix inequality (LMI). At long last, an illustrative model is given to show the performance and capability of the proposed strategy.

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 Robust Performance and Observer Based Control for Periodic Discrete-Time Uncertain Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Natália A. Keles ◽  
Márcio J. Lacerda ◽  
Cristiano M. Agulhari
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Estimation Error ◽  
Performance Criterion ◽  
Lyapunov Theory ◽  
Observer Design ◽  
Control Technique ◽  
Duality Principle ◽  
Linear Matrix ◽  
Periodic Linear

This paper presents an approach for the synthesis of observer-based controllers for discrete-time periodic linear systems. The H2 performance criterion has been employed to design both the observer and the controller. For the periodic observer design, two conditions in the form of Linear Matrix Inequalities (LMIs) are proposed, which stem from the Lyapunov Theory applied over the dynamics of the estimation error. The LMI condition obtained for the periodic state-feedback controller results from the application of the duality principle over the periodic system, under the assumption that only the estimated states are available to be used in the state-feedback compensation. Numerical experiments illustrate the potential of the proposed observer-based control technique.

Nonlinear observer based sliding mode control and oxygen fraction estimation for diesel engine

2017 ◽  
Vol 40 (7) ◽  
pp. 2227-2239 ◽  
Author(s):  
Haoping Wang ◽  
Qiankun Qu ◽  
Yang Tian
Keyword(s):  
Diesel Engine ◽  
Sliding Mode Control ◽  
Oxygen Concentration ◽  
Control Method ◽  
Sliding Mode ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Model Based ◽  
Mode Control

In this paper, a nonlinear observer based sliding mode control (NOSMC) approach for air-path and a model-based observer for oxygen concentration in the diesel engine equipped with a variable geometry turbocharger and exhaust gas recirculation is introduced. We propose a less conservative observer design technique for Lipschitz nonlinear systems using Ricatti equations. The observer gains are obtained by solving the linear matrix inequality (LMI). Then a robust nonlinear control method, sliding mode control is applied for the states of intake and exhaust manifold pressure and compressor mass flow rate for the sake of the minimization of emissions. The proposed NOSMC controller is applied on a mean value model of turbocharged diesel engine. Besides this, a model-based observer is developed to estimate the oxygen concentration in the intake and exhaust manifolds owing to its significance in reducing emissions of diesel engines. The validation and efficiency of the proposed method are demonstrated by AMESim and Matlab/Simulink co-simulation results.

scholarly journals Optimal guaranteed cost filtering for Markovian jump discrete-time systems

2004 ◽  
Vol 2004 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Peng Shi
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Estimation Error ◽  
Linear Matrix ◽  
State Estimator ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Discrete Time Systems ◽  
Linear State ◽  
Time Systems

This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

H 2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach

2011 ◽  
Author(s):  
Xin Wang ◽  
Edwin E. Yaz ◽  
Susan C. Schneider ◽  
Yvonne I. Yaz
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Time Step ◽  
Control Approach ◽  
The Difference

A novel H2–H∞ State Dependent Riccati Equation control approach is presented for providing a generalized control framework to discrete time nonlinear system. By solving a generalized Riccati Equation at each time step, the nonlinear state feedback control solution is found to satisfy mixed performance criteria guaranteeing quadratic optimality with inherent stability property in combination with H∞ type of disturbance attenuation. Two numerical techniques to compute the solution of the resulting Riccati equation are presented: The first one is based on finding the steady state solution of the difference equation at every step and the second one is based on finding the minimum solution of a linear matrix inequality. The effectiveness of the proposed techniques is demonstrated by simulations involving the control of an inverted pendulum on a cart, a benchmark mechanical system.

scholarly journals State Observer Design for Delayed Genetic Regulatory Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li-Ping Tian ◽  
Zhi-Jun Wang ◽  
Amin Mohammadbagheri ◽  
Fang-Xiang Wu
Keyword(s):  
Regulatory Network ◽  
Regulatory Networks ◽  
Estimation Error ◽  
State Observer ◽  
Genetic Regulatory Networks ◽  
Genetic Regulatory Network ◽  
Observer Design ◽  
Linear Matrix ◽  
Globally Asymptotically Stable ◽  
Internal States

Genetic regulatory networks are dynamic systems which describe the interactions among gene products (mRNAs and proteins). The internal states of a genetic regulatory network consist of the concentrations of mRNA and proteins involved in it, which are very helpful in understanding its dynamic behaviors. However, because of some limitations such as experiment techniques, not all internal states of genetic regulatory network can be effectively measured. Therefore it becomes an important issue to estimate the unmeasured states via the available measurements. In this study, we design a state observer to estimate the states of genetic regulatory networks with time delays from available measurements. Furthermore, based on linear matrix inequality (LMI) approach, a criterion is established to guarantee that the dynamic of estimation error is globally asymptotically stable. A gene repressillatory network is employed to illustrate the effectiveness of our design approach.

scholarly journals A comparative study of nonlinear circle criterion based observer and H∞ observer for induction motor drive

2019 ◽  
Vol 10 (3) ◽  
pp. 1229
Author(s):  
Farid Berrezzek ◽  
Wafa Bourbia ◽  
Bachir Bensaker
Keyword(s):  
Comparative Study ◽  
Induction Motor ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Lmi Optimization ◽  
Circle Criterion ◽  
True State ◽  
The Stability

<span lang="EN-US">This paper deals with a comparative study of circle criterion based nonlinear observer<em> </em>and <em>H<sub>∞</sub></em> observer for induction motor (IM) drive. The  advantage of the circle criterion approach for nonlinear observer design is that it directly handles the nonlinearities of the system with less restriction  conditions in contrast of the other methods which attempt to eliminate them. However the <em>H<sub>∞</sub></em> observer guaranteed the stability taking into account disturbance and noise attenuation. Linear matrix inequality (LMI) optimization approach is used to compute the gains matrices for the two observers. The simulation results show the superiority of <em>H<sub>∞</sub></em> observer in the sense that it can achieve convergence to the true state, despite the nonlinearity of model and the presence of disturbance.</span>

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