Temat: Linear-quadratic problems - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Optimal control of a two-dimensional linear system with a quadratic performance index with constraints on the trajectory and the control
Autorzy:: Biły, Barbara
Powiązania:: https://bibliotekanauki.pl/articles/747527.pdf
Data publikacji:: 1997
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Linear-quadratic problems
Other methods
Opis:: .
The main purpose of this note is to present a method for solving the linear-quadratic optimal regulator for discrete, linear general two-dimensional system with constant coefficients. The quadratic optimal regulator problem can be formulated: find of sequence of control vectors in fixed rectangle, which transfer the system to given final state vector and minimizes the quadratic performance index, with constraints of control and state vector. This problem, by transformation for systemand performance index is reduced to equivalent mathematical programming problem. Necessary and sufficient conditions are established for the existence of a solution to this problem. With slight modifications the considerations can be extended for 2-D systems with variable coefficient and n-D linear systems.
Źródło:: Mathematica Applicanda; 1997, 26, 40
1730-2668
2299-4009
Pojawia się w:: Mathematica Applicanda
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Optimal control for a nonstationary linear system with a quadratic cost functional
Autorzy:: Czornik, Adam
Powiązania:: https://bibliotekanauki.pl/articles/747535.pdf
Data publikacji:: 1997
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Optimal stochastic control
Problems involving randomness
Linear-quadratic problems
Opis:: .
This paper is about optimal control of infinite-horizon nonstationary stochastic linear processes with a quadratic cost criterion. The synthesis problem of optimal control is solved under the assumptions that the criterion is an average expected cost and that the process' matrices possess limits for the time approaching infinity. Furthermore, the limit matrices are such that the "limit" process is both observable and controllable. The paper documents existence of an optimal feedback control policy. The policy is such that the gain matrix is a (scaled) solution to a Riccati stationary matrix equation. The equation is stationary in that its coefficients are the limits of the process' non-stationary matrices.
Źródło:: Mathematica Applicanda; 1997, 26, 40
1730-2668
2299-4009
Pojawia się w:: Mathematica Applicanda
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Error estimates for finite element approximations of elliptic control problems
Autorzy:: Alt, Walter
Bräutigam, Nils
Rösch, Arnd
Powiązania:: https://bibliotekanauki.pl/articles/729441.pdf
Data publikacji:: 2007
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Linear quadratic optimal control problems
elliptic equations
finite element approximations
error estimates
Opis:: We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 1; 7-22
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints
Autorzy:: Meyer, C.
Powiązania:: https://bibliotekanauki.pl/articles/971011.pdf
Data publikacji:: 2008
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: równanie eliptyczne
aproksymacja numeryczna
linear quadratic optimal control problems
elliptic equations
state constraints
numerical approximation
Opis:: We consider a linear-quadratic elliptic optimal control problem with pointwise state constraints. The problem is fully discretized using linear ansatz functions for state and control. Based on a Slater-type argument, we investigate the approximation behavior for mesh size tending to zero. The obtained convergence order for the L²-error of the control and for H 1-error of the state is 1 - ε in the two-dimensional case and 1/2 - ε in three dimensions, provided that the domain satisfies certain regularity assumptions. In a second step, a state-constrained problem with additional control constraints is considered. Here, the control is discretized by constant ansatz functions. It is shown that the convergence theory can be adapted to this case yielding the same order of convergence. The theoretical findings are confirmed by numerical examples.
Źródło:: Control and Cybernetics; 2008, 37, 1; 51-83
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Finite element error analysis for state-constrained optimal control of the Stokes equations
Autorzy:: Los Reyes, J. C. de
Meyer, C.
Vexler, B.
Powiązania:: https://bibliotekanauki.pl/articles/969607.pdf
Data publikacji:: 2008
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: równanie Stokesa
aproksymacja numeryczna
element skończony
linear quadratic optimal control problems
Stokes equations
state constraints
numerical approximation
finite elements
Opis:: An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the L∞-finite-eleinent-error can be verified for different numerical settings. Finally the results of two numerical experiments are presented.
Źródło:: Control and Cybernetics; 2008, 37, 2; 251-284
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

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