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    Wyświetlanie 1-12 z 12
    Tytuł:
    Shape optimization for stationary Navier-Stokes equations
    Autorzy:
    Halanay, A.
    Tiba, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/970751.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal design
    optimal control method
    fluid mechanics
    penalization
    gradient method
    Opis:
    This work discusses geometric optimization problems governed by stationary Navier-Stokes equations. Optimal domains are proved to exist under the assumption that the family of admissible domains is bounded and satisfies the Lipschitz condition with a uniform constant, and in the absence of the uniqueness property for the state system. Through the parametrization of the admissible shapes by continuous functions defined on a larger universal domain, the optimization parameter becomes a control, i.e. an element of that family of continuous functions. The approximating extension technique via the penalization of the Navier-Stokes equation enables the approximation of the associated shape optimization problem by an optimal control problem. Results on existence and uniqueness are proved for the approximating problem and a gradient-type algorithm is indicated.
    Źródło:
    Control and Cybernetics; 2009, 38, 4B; 1359-1374
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Discrete relaxed method for semilinear parabolic optimal control problem
    Autorzy:
    Chryssoverghi, I.
    Coletsos, J.
    Kokkinis, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/205973.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne
    accumulation points
    discrete optimisation method
    discretization
    distributed control
    minimum principle
    optimal control
    parabolic equations
    partial differential equations
    penalty method
    relaxed control
    semilinear parabolic system
    Opis:
    We consider an optimal control problem for systems governed by semilinear parabolic partial differential equations with control and state constraints, without any convexity assumptions. A discrete optimization method is proposed to solve this problem in its relaxed form which combines a penalized Armijo type method with a finite element discretization and constructs sequences of discrete Gamkrelidze relaxed controls. Under appropriate assumptions, we prove that accumulation points of these sequences satisfy the relaxed Pontryagin necessary conditions for optimality. Moreover, we show that the Gamkrelidze controls thus generated can be replaced by simulating piecewise constant classical controls.
    Źródło:
    Control and Cybernetics; 1999, 28, 2; 157-176
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Design of a novel control algorithm for a 6 D.O.F. mobile manipulator based on a robust observer
    Autorzy:
    Bolandi, H.
    Ehyaei, A. F.
    Esmaeilzadeh, A. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970986.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    robust control
    mobile manipulator
    generalized-α method
    robust observer
    Opis:
    In this paper a control algorithm based on a design technique named "Robust Damping Control" is introduced. A robust observer is further shown to overcome the problem of using velocity sensors that may degrade the system performance. The proposed controller uses only position measurements and is capable of disturbance rejection in the presence of unknown bounded disturbances without requiring the knowledge of its bound. Moreover, we propose an accurate and fast time integration method to solve the dynamic equations of the mobile manipulator system. The simulation results of a 6 D.O.F. mobile manipulator illustrate the effectiveness of the presented algorithm.
    Źródło:
    Control and Cybernetics; 2005, 34, 4; 1057-1074
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximation of optimal control problems with bound constraints by control parameterization
    Autorzy:
    Alt, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/970516.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne nieliniowe
    metoda Newtona
    nonlinear optimal control
    bound constraints
    Newton's method
    control parameterization
    Opis:
    We consider nonlinear optimal control problems with bound constraints for the controls. Under the assumption that the optimal control is continuous and has finitely many smooth boundary arcs, we show that the system of optimahty conditions can be reduced to a system of operator equations. Based on this system we investigate convergence of approximations by control parameterization.
    Źródło:
    Control and Cybernetics; 2003, 32, 3; 451-472
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of the Lagrange-SQP-Newton method for the control of a phase field equation
    Autorzy:
    Heinkenschloss, M.
    Troeltzsch, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/206519.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równania paraboliczne
    równania różniczkowe
    stabilność
    sterowanie optymalne
    control constraints
    Lagrange-SQP-Newton method
    optimal control
    phase field equation
    programming method
    sequential quadratic
    Opis:
    This paper investigates the local convergence of the Lagrange-SQP-Newton method applied to an optimal control problem governed by a phase field equation with distributed control. The phase field equation is a system of two semilinear parabolic differential equations. Stability analysis of optimization problems and regularity results for parabolic differential equations are used to proof convergence of the controls with respect to the L[sup 2](Q) norm and with respect to the L[sup infinity](Q) norm.
    Źródło:
    Control and Cybernetics; 1999, 28, 2; 177-211
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Metric regularity under approximations
    Autorzy:
    Dontchev, A. L.
    Veliov, V. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970750.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    metric regularity
    inexact iterative methods
    Newton method
    proximal point method
    discrete approximation
    optimal control
    Opis:
    In this paper we show that metric regularity and strong metric regularity of a set-valued mapping imply convergence of inexact iterative methods for solving a generalized equation associated with this mapping. To accomplish this, we first focus on the question how these properties are preserved under changes of the mapping and the reference point. As an application, we consider discrete approximations in optimal control.
    Źródło:
    Control and Cybernetics; 2009, 38, 4B; 1283-1303
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximate relaxed descent method for optimal control problems
    Autorzy:
    Chryssoverghi, I.
    Coletsos, J.
    Kokkinis, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/206679.pdf
    Data publikacji:
    2001
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    dyskretyzacja
    kontrola relaksacyjna
    sterowanie optymalne
    descent method
    discretization
    optimal control
    relaxed controls
    Opis:
    We consider an optimal control problem for systems governed by ordinary differential equations with control constraints. Since no convexity assumptions are made on the data, the problem is reformulated in relaxed form. The relaxed state equation is discretized by the implicit trapezoidal scheme and the relaxed controls are approximated by piecewise constant relaxed controls. We then propose a combined descent and discretization method that generates sequences of discrete relaxed controls and progressively refines the discretization. Since here the adjoint of the discrete state equation is not defined, we use, at each iteration, an approximate derivative of the cost functional defined by discretizing the continuous adjoint equation and the integral involved by appropriate trapezoidal schemes. It is proved that accumulation points of sequences constructed by this method satisfy the strong relaxed necessary conditions for optimality for the continuous problem. Finally, the computed relaxed controls can be easily approximated by piecewise constant classical controls.
    Źródło:
    Control and Cybernetics; 2001, 30, 4; 385-404
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Distributed optimal control problems driven by space-time fractional parabolic equations
    Autorzy:
    Mehandiratta, Vaibhav
    Mehra, Mani
    Leugering, Günter
    Powiązania:
    https://bibliotekanauki.pl/articles/2183495.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    space-time fractional parabolic equations
    Caputo fractional derivative
    distributed control
    L1 method
    Grünwald-Letnikov formula
    Opis:
    We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial fractional derivatives of Sturm-Liouville type. We first prove existence and uniqueness of solutions of STFPEs on an open bounded interval and study their regularity. Then we show existence and uniqueness of solutions to a quadratic distributed optimal control problem. We derive an adjoint problem using the right-Caputo derivative in time and provide optimality conditions for the control problem. Moreover, we propose a finite difference scheme to find the approximate solution of the considered optimal control problem. In the proposed scheme, the well-known L1 method has been used to approximate the time-fractional Caputo derivative, while the spatial derivative is approximated using the Grünwald-Letnikov formula. Finally, we demonstrate the accuracy and the performance of the proposed difference scheme via examples.
    Źródło:
    Control and Cybernetics; 2022, 51, 2; 191--226
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Nash equilibrium approach for multiobjective optimal control problems with elliptic partial differential equations
    Autorzy:
    Dreves, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/206122.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    multiobjective optimization
    generalized Nash equilibrium
    optimal control problem
    elliptic partial differential equation
    finite elements
    interior point method
    Opis:
    We consider the generalized Nash equilibrium as a solution concept for multiobjective optimal control problems governed by elliptic partial differential equations with constraints not only for the control but also for the state variables. In the first part, we present a constructive proof of the existence of a generalized Nash equilibrium via an approximating sequence of suitable finite dimensional discretizations. In the second part, we propose a variant of a potential reduction algorithm for the numerical solution of these discretized problems. In contrast to the existing numerical approaches ours does not require the computation of the control–to–state mapping. Instead we introduce different state variables and guarantee that they become equal at a solution. We prove sufficient conditions for the convergence of our algorithm to a solution. Furthermore, some numerical results showing the applicability are provided.
    Źródło:
    Control and Cybernetics; 2016, 45, 4; 457-482
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximate gradient projection method with general Runge-Kutta schemes and piecewise polynomial controls for optimal control problems
    Autorzy:
    Chryssoverghi, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/970094.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    dyskretyzacja
    sterowanie optymalne
    optimal control
    gradient projection method
    discretization
    non-matching Runge-Kutta schemes
    piecewise polynomial controls
    Opis:
    This paper addresses the numerical solution of optimal control problems for systems described by ordinary differential equations with control constraints. The state equation is discretized by a general explicit Runge-Kutta scheme and the controls are approximated by functions that are piecewise polynomial, but not necessarily continuous. We then propose an approximate gradient projection method that constructs sequences of discrete controls and progressively refines the discretization. Instead of using the exact discrete cost derivative, which usually requires tedious calculations, we use here an approximate derivative of the cost functional denned by discretizing the continuous adjoint equation by the same Runge-Kutta scheme backward and the integral involved by a Newton-Cotes integration rule, both involving maximal order intermediate approximations. The main result is that strong accumulation points in L2, if they exist, of sequences generated by this method satisfy the weak necessary conditions for optimality for the continuous problem. In the unconstrained case and under additional assumptions, we prove strong convergence in L2 and derive an a posteriori error estimate. Finally, numerical examples are given.
    Źródło:
    Control and Cybernetics; 2005, 34, 2; 425-451
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary optimal control problem for the phase-field transition system using fractional steps method
    Zadanie sterowania optymalnego brzegiem dla układu pola ze zmianą fazy z wykorzystaniem metody kroków ułamkowych
    Autorzy:
    Moroşanu, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/206721.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    zagadnienie ze swobodnym brzegiem
    sterowanie optymalne
    metoda kroków ułamkowych
    warunki optymalności
    metoda elementu skończonego
    metoda gradientowa
    układ ze zmianą fazy
    phase-field transition system
    free boundary problem
    optimal control
    fractional steps method
    optimality conditions
    finite element method
    gradient method
    Opis:
    In this paper we prove the convergence of an iterative scheme of fractional steps type for boundary optimal control problem which is governed by the phase-field transition system. The existence of an optimal control and necessary optimality conditions are given for approximating problem. A gradient type algorithm and numerical implementation of this algorithm are discussed.
    W artykule dowodzi się zbieżności procedury iteracyjnej typu kroków ułamkowych dla zagadnienia sterowania optymalnego brzegiem w układzie pola ze zmianą fazy. Wykazano istnienie sterowania optymalnego i podano warunki konieczne optymalności dla zagadnienia aproksymującego. Rozpatrzono odpowiedni algorytm gradientowy oraz realizację numeryczną tego algorytmu.
    Źródło:
    Control and Cybernetics; 2003, 32, 1; 5-32
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Error estimates for the finite-element approximation of a semilinear elliptic control problem
    Autorzy:
    Casas, E.
    Troeltzsch, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/206743.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    aproksymacja numeryczna
    metoda elementu skończonego
    równanie eliptyczne półliniowe
    sterowanie rozproszone
    distributed control
    error estimates
    finite element method
    numerical approximation
    semilinear elliptic equation
    Opis:
    We consider the finite-element approximation of a distributed optimal control problem governed by a semilinear elliptic partial differential equation, where pointwise constraints on the control are given. We prove the existence of local approximate solutions converging to a given local reference solution. Moreover, we derive error estimates for local solutions in the maximum norm.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 695-712
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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