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An application of the Fourier transform to optimization of continuous 2-D systems

Vitali Dymkou, Michael Dymkov (2003)

International Journal of Applied Mathematics and Computer Science

This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.

An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Alexey Zhirabok, Alexey Shumsky (2012)

International Journal of Applied Mathematics and Computer Science

The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,...

An asymptotic state observer for a class of nonlinear delay systems

Alfredo Germani, Costanzo Manes, Pierdomenico Pepe (2001)

Kybernetika

The problem of state reconstruction from input and output measurements for nonlinear time delay systems is studied in this paper and a state observer is proposed that is easy to implement and, under suitable assumptions on the system and on the input function, gives exponential observation error decay. The proposed observer is itself a delay system and can be classified as an identity observer, in that it is such that if at a given time instant the system and observer states coincide, on a suitable...

An autonomous vehicle sequencing problem at intersections: A genetic algorithm approach

Fei Yan, Mahjoub Dridi, Abdellah El Moudni (2013)

International Journal of Applied Mathematics and Computer Science

This paper addresses a vehicle sequencing problem for adjacent intersections under the framework of Autonomous Intersection Management (AIM). In the context of AIM, autonomous vehicles are considered to be independent individuals and the traffic control aims at deciding on an efficient vehicle passing sequence. Since there are considerable vehicle passing combinations, how to find an efficient vehicle passing sequence in a short time becomes a big challenge, especially for more than one intersection....

An averaging principle for stochastic evolution equations. II.

Bohdan Maslowski, Jan Seidler, Ivo Vrkoč (1991)

Mathematica Bohemica

In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.

An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

Jiawen Bian, Huiming Peng, Jing Xing, Zhihui Liu, Hongwei Li (2013)

International Journal of Applied Mathematics and Computer Science

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton-Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton-Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators...

An efficient computation of the solution of the block decoupling problem with coefficient assignment over a ring

Jean Assan, Anna Maria Perdon (1999)

Kybernetika

The paper presents procedures to check solvability and to compute solutions to the Block Decoupling Problem over a Noetherian ring and procedures to compute a feedback law that assigns the coefficients of the compensated system while mantaining the decoupled structure over a Principal Ideal Domain. The algorithms have been implemented using MapleV® and CoCoA [CoCoA].

An elastic membrane with an attached non-linear thermoelastic rod

Werner Horn, Jan Sokołowski (2002)

International Journal of Applied Mathematics and Computer Science

We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain Ω ⊂ R^2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence...

An equivalent matrix pencilfor bivariate polynomial matrices

Mohamed Boudellioua (2006)

International Journal of Applied Mathematics and Computer Science

In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

An estimation of the controllability time for single-input systems on compact Lie Groups

Andrei Agrachev, Thomas Chambrion (2006)

ESAIM: Control, Optimisation and Calculus of Variations

Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters...

An example of the knowledge based controller-design and evaluation.

Oto Tezak (1999)

Mathware and Soft Computing

Knowledge based controller for a balance control model is presented in this paper. The design of the controller was based on the human control of the same process. Developed controller is tested by means of simulation and operation on the laboratory balance control model. The simulation results of the controller as well as a statistical description of the experiments with developed controller and human control is presented in the paper. Verification is based on experiments with an intelligent controller...

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