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An algebraic theory of order

Philippe Chartier, Ander Murua (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified)...

An algorithm for reducing the dimension and size of a sample for data exploration procedures

Piotr Kulczycki, Szymon Łukasik (2014)

International Journal of Applied Mathematics and Computer Science

The paper deals with the issue of reducing the dimension and size of a data set (random sample) for exploratory data analysis procedures. The concept of the algorithm investigated here is based on linear transformation to a space of a smaller dimension, while retaining as much as possible the same distances between particular elements. Elements of the transformation matrix are computed using the metaheuristics of parallel fast simulated annealing. Moreover, elimination of or a decrease in importance...

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 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 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...

An extension of the Cayley-Hamilton theorem for nonlinear time-varying systems

Tadeusz Kaczorek (2006)

International Journal of Applied Mathematics and Computer Science

The classical Cayley-Hamilton theorem is extended to nonlinear time-varying systems with square and rectangular system matrices. It is shown that in both cases system matrices satisfy many equations with coefficients being the coefficients of characteristic polynomials of suitable square matrices. The proposed theorems are illustrated with numerical examples.

An H ∞ sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults

Ali Ben Brahim, Slim Dhahri, Fayçal Ben Hmida, Anis Sellami (2015)

International Journal of Applied Mathematics and Computer Science

This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two...

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