scholarly journals Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 88
Author(s):  
Andreas Rauh ◽  
Auguste Bourgois ◽  
Luc Jaulin
Keyword(s):  
Discrete Time ◽  
State Observer ◽  
Observer Design ◽  
State Variables ◽  
Computationally Efficient ◽  
True Solution ◽  
Bounded Error ◽  
Quasi Linear System ◽  
Outer Bounds ◽  
Predictor Corrector

Thick ellipsoids were recently introduced by the authors to represent uncertainty in state variables of dynamic systems, not only in terms of guaranteed outer bounds but also in terms of an inner enclosure that belongs to the true solution set with certainty. Because previous work has focused on the definition and computationally efficient implementation of arithmetic operations and extensions of nonlinear standard functions, where all arguments are replaced by thick ellipsoids, this paper introduces novel operators for specifically evaluating quasi-linear system models with bounded parameters as well as for the union and intersection of thick ellipsoids. These techniques are combined in such a way that a discrete-time state observer can be designed in a predictor-corrector framework. Estimation results are presented for a combined observer-based estimation of state variables as well as disturbance forces and torques in the sense of an unknown input estimator for a hovercraft.

Output Adaptive Observers Design for Linear Non-Stationary Systems with Polynomial Parameters

2021 ◽  
Vol 22 (8) ◽  
pp. 404-410
Author(s):  
K. B. Dang ◽  
A. A. Pyrkin ◽  
A. A. Bobtsov ◽  
A. A. Vedyakov ◽  
S. I. Nizovtsev
Keyword(s):  
Linear Time ◽  
State Observer ◽  
Observer Design ◽  
Model Parameters ◽  
Time Varying ◽  
State Variables ◽  
Unknown Constant ◽  
Established Method ◽  
Time Varying Parameters ◽  
True Values

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

Discrete-Time Well-Conditioned State Observer Design and Evaluation

2001 ◽  
Vol 123 (4) ◽  
pp. 615-622 ◽  
Author(s):  
Kunsoo Huh ◽  
Jongchul Jung ◽  
Jeffrey L. Stein
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Poor Performance ◽  
State Observer ◽  
Observer Design ◽  
False Alarms ◽  
Conditioning Factors ◽  
Estimation Performance ◽  
Filter Performance ◽  
Ill Conditioning

Model-based monitoring systems based on state observer theory often have poor performance with respect to accuracy, bandwidth, reliability (false alarms), and robustness. The above limitations are closely related to the ill-conditioning factors such as transient characteristics due to unknown initial values and round-off errors, and steady-state accuracy due to plant perturbations and sensor bias. In this paper, by minimizing the effects of the ill-conditioning factors, a well-conditioned observer is proposed for the discrete-time systems. A performance index is determined to represent the quantitative effects of the ill-conditioning factors and two design methods are described for the well-conditioned observers. The estimation performance of the well-conditioned observers is verified in simulations where transient as well as steady-state error robustness to perturbations is shown to be better than or equal to Kalman filter performance depending on the nature of modeling errors. The estimation performance is also demonstrated on an experimental setup designed and built for this purpose.

scholarly journals An LMI-Based H ∞ Discrete-Time Nonlinear State Observer Design for an Anaerobic Digestion Model

2017 ◽  
Vol 50 (1) ◽  
pp. 11547-11552
Author(s):  
K. Chaib Draa ◽  
H. Voos ◽  
M. Alma ◽  
A. Zemouche ◽  
M. Darouach
Keyword(s):  
Anaerobic Digestion ◽  
Discrete Time ◽  
State Observer ◽  
Observer Design ◽  
Nonlinear State

State observer design for a class of Takagi-Sugeno discrete-time descriptor systems

2015 ◽  
Vol 9 ◽  
pp. 5871-5885
Author(s):  
Ilham Hmaiddouch ◽  
Boutayna Bentahra ◽  
Abdellatif El Assoudi ◽  
Jalal Soulami ◽  
El Hassane El Yaagoubi
Keyword(s):  
Discrete Time ◽  
State Observer ◽  
Observer Design ◽  
Descriptor Systems ◽  
Takagi Sugeno

A fresh approach to the design of observers for time-delay systems

2016 ◽  
Vol 40 (2) ◽  
pp. 477-503 ◽  
Author(s):  
Dinh Cong Huong
Keyword(s):  
Time Delay ◽  
State Vector ◽  
State Observer ◽  
The State ◽  
Observer Design ◽  
Delay Systems ◽  
Time Delay Systems ◽  
State Variables ◽  
State Transformation ◽  
Original State

This paper presents a fresh approach to the design of state observers for a class of time-delay systems with one time delay in the state and output vectors. By proposing a new coordinate state transformation, the system is first transformed into the new coordinates where all the delay terms associated with the state variables are injected into the system’s output and input. Thus, in the new coordinate system, a Luenberger-type state observer can be easily designed. Then, a backward state transformation problem is studied which allows us to reconstruct the original state vector of the system. Conditions for the existence of the state transformations and an algorithm for computing them are provided in this paper. We show that our approach works for a wider class of time-delay systems in the sense that when some existing state observer design methods fail to reconstruct the state vector, the proposed new change of coordinates and the observer scheme in this paper can still reconstruct the original state vector. Numerical examples and simulation results are given to illustrative the effectiveness of the proposed design approach.

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

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