scholarly journals A Concise Review of State Estimation Techniques for Partial Differential Equation Systems

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3180
Author(s):  
Ivan Francisco Yupanqui Yupanqui Tello ◽  
Alain Vande Vande Wouwer ◽  
Daniel Coutinho
Keyword(s):  
Differential Equation ◽  
State Estimation ◽  
Point Of View ◽  
Distributed Parameter ◽  
Theoretical Point ◽  
Partial Differential ◽  
Estimation Techniques ◽  
Ode Models ◽  
State Observers ◽  
Pde Systems

While state estimation techniques are routinely applied to systems represented by ordinary differential equation (ODE) models, it remains a challenging task to design an observer for a distributed parameter system described by partial differential equations (PDEs). Indeed, PDE systems present a number of unique challenges related to the space-time dependence of the states, and well-established methods for ODE systems do not translate directly. However, the steady progresses in computational power allows executing increasingly sophisticated algorithms, and the field of state estimation for PDE systems has received revived interest in the last decades, also from a theoretical point of view. This paper provides a concise overview of some of the available methods for the design of state observers, or software sensors, for linear and semilinear PDE systems based on both early and late lumping approaches.

SYSTEM CHARACTERISTICS OF DISTRIBUTED PARAMETER SYSTEMS

2020 ◽  
Vol 70 (3) ◽  
pp. 34-44
Author(s):  
Kamen Perev
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Initial Conditions ◽  
Distributed Parameter Systems ◽  
Point Of View ◽  
Distributed Parameter ◽  
Partial Differential ◽  
Special Cases ◽  
The Green Function ◽  
Set Up

The paper considers the problem of distributed parameter systems modeling. The basic model types are presented, depending on the partial differential equation, which determines the physical processes dynamics. The similarities and the differences with the models described in terms of ordinary differential equations are discussed. A special attention is paid to the problem of heat flow in a rod. The problem set up is demonstrated and the methods of its solution are discussed. The main characteristics from a system point of view are presented, namely the Green function and the transfer function. Different special cases for these characteristics are discussed, depending on the specific partial differential equation, as well as the initial conditions and the boundary conditions.

Identification of Systems Described by Partial Differential Equations

1966 ◽  
Vol 88 (2) ◽  
pp. 463-468 ◽  
Author(s):  
F. J. Perdreauville ◽  
R. E. Goodson
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Equation Model ◽  
Distributed Parameter ◽  
Differential Equation Model ◽  
Partial Differential ◽  
Varying Coefficients ◽  
Partial Differential Equation Model ◽  
Linear And Nonlinear

A method is given for the identification of distributed parameter systems. Normal operating records or experimental data may be used. The method involves the determination of arbitrary parameters in an assumed partial differential-equation model of the system. The method applies equally well to linear and nonlinear equations, and equations with varying coefficients. The accuracy of the results depends upon the exactness of the model, the amount of data used, the error in numerical integration, and the amount of noise which is present in the data. Examples are given which illustrate the application of the method. Results using the method for the identification of a physical system are given.

scholarly journals Computer simulation of the pulse-periodic electric field effect on the 2D director orientation of nematic liquid crystal. Experimental research of multimode nematic liquid crystal waveguides.

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A.S. Ayriyan ◽  
◽  
E.A. Ayryan ◽  
A.A. Egorov ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Electric Field ◽  
Nematic Liquid Crystal ◽  
Experimental Research ◽  
Point Of View ◽  
Dynamic Processes ◽  
Theoretical Point ◽  
Two Dimensional

In this paper, we numerically investigate a two-dimensional differential equation describing the motion of a director of a nematic liquid crystal for the case of an alternating external electric field. The presence of the previously discovered accumulation effect has been confirmed by numerical modeling. A comparison is made with the case of a constant electric field, and also a qualitative comparison with an experiment is given. Incomplete agreement with experimental data indicates the need for further research. However, it should be noted that the constructed mathematical model of the phenomenon allows at this stage to obtain estimates that are sufficiently acceptable for experiment and correctly predict the dynamics of processes in liquid crystals. An analysis of the features of the propagation of quasi-waveguide modes in a liquid crystal waveguide showed that, in the case of dynamic processes, such effects as power exchange between coupled modes, leakage of modes, re-emission of modes into modes of a different order, etc., can be observed. The programs for numerical solution and computer modeling of two-dimensional parabolic partial differential equation were developed both in FORTRAN and C/C++. The results obtained are important for further investigation of dynamic processes inside non-stationary liquid crystal layers, both from a theoretical point of view for understanding kinetic processes in liquid crystals and from a practical point of view when organizing and conducting different experimental research.

PID Control System for a Distributed Parameter Process

2014 ◽  
Vol 555 ◽  
pp. 222-231 ◽  
Author(s):  
Mihaela Ligia Ungureşan ◽  
Vlad Mureşan
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Partial Differential Equation ◽  
Control System ◽  
Control Systems ◽  
Pid Control ◽  
Distributed Parameter ◽  
Partial Differential ◽  
Pid Algorithm

This paper presents the numerical simulation of a control system, with PID algorithm, for a process modeled through a partial differential equation of second order (PDE II.2), with respect to time (t) and to a spatial variable (p). Because these types of control systems are less usual, this paper develops a case study, with a program run on the computer. The details of using the PID control are pointed out, for an example of a system which contains a process with PDE II.2 structure.

Exact and approximate controllability for distributed parameter systems

Acta Numerica ◽  
1994 ◽  
Vol 3 ◽  
pp. 269-378 ◽  
Author(s):  
R. Glowinski ◽  
J.L. Lions
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Approximate Controllability ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Partial Differential ◽  
Control Functions

We consider a system whose state is given by the solution y to a Partial Differential Equation (PDE) of evolution, and which contains control functions, denoted by v.

Timber Auctions in the Context of the Modern Auction Theory

2007 ◽  
pp. 86-94
Author(s):  
A. Manakov
Keyword(s):  
Theoretical Analysis ◽  
Auction Theory ◽  
Point Of View ◽  
Theoretical Point ◽  
English Auction ◽  
Analysis And Evaluation

The article provides theoretical analysis and evaluation of the timber auctions reforms in Russia. The author shows that the mechanism of the "combined auctions", which functioned until recently, is more appropriate from the theoretical point of view (and from the point of view of the Russian practice) as compared to the officially approved format of the English auction.

A novel cryptosystem based on abstract automata and Latin cubes

2015 ◽  
Vol 52 (2) ◽  
pp. 221-232
Author(s):  
Pál Dömösi ◽  
Géza Horváth
Keyword(s):  
Block Cipher ◽  
Finite Automata ◽  
Theoretical Background ◽  
Point Of View ◽  
Theoretical Point ◽  
Transition Matrices ◽  
Encryption And Decryption ◽  
Secret Keys ◽  
Automata Network ◽  
Fully Functioning

In this paper we introduce a novel block cipher based on the composition of abstract finite automata and Latin cubes. For information encryption and decryption the apparatus uses the same secret keys, which consist of key-automata based on composition of abstract finite automata such that the transition matrices of the component automata form Latin cubes. The aim of the paper is to show the essence of our algorithms not only for specialists working in compositions of abstract automata but also for all researchers interested in cryptosystems. Therefore, automata theoretical background of our results is not emphasized. The introduced cryptosystem is important also from a theoretical point of view, because it is the first fully functioning block cipher based on automata network.

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