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Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions

Yousef Edrisi Tabriz, Mehrdad Lakestani (2015)

Kybernetika

In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon B-spline functions. The properties of B-spline functions are presented. The operational matrix of derivative ( 𝐃 φ ) and integration matrix ( 𝐏 ) are introduced. These matrices are utilized to reduce the solution of nonlinear constrained quadratic optimal control to the solution of nonlinear programming one to which existing well-developed...

Discrete smoothing splines and digital filtration. Theory and applications

Jiří Hřebíček, František Šik, Vítězslav Veselý (1990)

Aplikace matematiky

Two universally applicable smoothing operations adjustable to meet the specific properties of the given smoothing problem are widely used: 1. Smoothing splines and 2. Smoothing digital convolution filters. The first operation is related to the data vector r = ( r 0 , . . . , r n - 1 ) T with respect to the operations 𝒜 , and to the smoothing parameter α . The resulting function is denoted by σ α ( t ) . The measured sample r is defined on an equally spaced mesh Δ = { t i = i h } i = 0 n - 1 ...

Dislocation dynamics - analytical description of the interaction force between dipolar loops

Vojtěch Minárik, Jan Kratochvíl (2007)

Kybernetika

The interaction between dislocation dipolar loops plays an important role in the computation of the dislocation dynamics. The analytical form of the interaction force between two loops derived in the present paper from Kroupa’s formula of the stress field generated by a single dipolar loop allows for faster computation.

Dynamics of an artificial slope

Bartoň, Stanislav (2021)

Programs and Algorithms of Numerical Mathematics

The slope shape is replaced by a 3D regression function which corresponds with high precision to the position of several hundred points which were determined on the surface of the slope body. The position of several points was repeatedly measured for several years. The time changes in the position of these points were used to create regression functions that describe vertical movements, slope settlement and horizontal movements, slope movement. The model results are presented in the form of mathematical...

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