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Wyświetlanie 1-15 z 16
Tytuł:
Controllability of semilinear wave equations with infinitely iterated logarithms
Autorzy:
Cannarsa, P.
Komornik, V.
Loreti, P.
Powiązania:
https://bibliotekanauki.pl/articles/206588.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
controllability
semilinear equation
wave equation
Opis:
In a previous work we improved some earlier results of Imanuvilov, Li and Zhang, and of Zuazua, on the boundary exact controllability of semilinear wave equations by weakening the growth assumptions on the nonlinearity. Answering a question of Zuazua we give a still weaker, essentially optimal condition. Furthermore, we establish an approximate internal controllability result under the same growth assumptions.
Źródło:
Control and Cybernetics; 1999, 28, 3; 449-461
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllability of a model of combined anticancer therapy
Autorzy:
Klamka, J.
Świerniak, A.
Powiązania:
https://bibliotekanauki.pl/articles/206596.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
controllability
semilinear systems
biomathematical modelling
cancer therapy
Opis:
Controllability of combination of antiangiogenic treatment and chemotherapy is considered. A model used in the paper is a finite-dimensional dynamical control system described by secondo order semilinear time invariant ordinary differential state equations. Using a generalized open mapping theorem, sufficient conditions for constrained local controllability in a given time interval are formulated and proved. These conditions require verification of constrained global controllability of the associated linear second-order dynamical control system.
Źródło:
Control and Cybernetics; 2013, 42, 1; 123-138
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient conditions for unique global solutions in optimal control of semilinear equations with C1 nonlinearity
Autorzy:
Ahmad Ali, Ahmad
Deckelnick, Klaus
Hinze, Michael
Powiązania:
https://bibliotekanauki.pl/articles/1839143.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
semilinear PDE
uniqueness of global solutions
Opis:
We consider a semilinear elliptic optimal control problem possibly subject to control and/or state constraints. Generalizing previous work, presented in Ahmad Ali, Deckelnick and Hinze (2016) we provide a condition which guarantees that a solution of the necessary first order conditions is a global minimum. A similiar result also holds at the discrete level where the corresponding condition can be evaluated explicitly. Our investigations are motivated by G¨unter Leugering, who raised the question whether the problem class considered in Ahmad Ali, Deckelnick and Hinze (2016) can be extended to the nonlinearity φ(s) = s|s|. We develop a corresponding analysis and present several numerical test examples demonstrating its usefulness in practice.
Źródło:
Control and Cybernetics; 2019, 48, 2; 325-344
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions
Autorzy:
Krug, Richard
Leugering, Günter
Martin, Alexander
Schmidt, Martin
Weninger, Dieter
Powiązania:
https://bibliotekanauki.pl/articles/2183473.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
time-domain decomposition
optimal control
semilinear hyperbolic systems
convergence
Opis:
In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.
Źródło:
Control and Cybernetics; 2021, 50, 4; 427--455
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact controllability for the semilinear string equation in non cylindrical domains
Autorzy:
Araruna, F. D.
Antunes, G. O.
Medeiros, L. A.
Powiązania:
https://bibliotekanauki.pl/articles/970361.pdf
Data publikacji:
2004
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowność
półliniowość
exact controllability
string equation
semilinear
non cylindrical
Opis:
In this paper, we investigate the exact controllability for a mixed problem for the equation u^n - [...] + f(u) = 0 in a non cylindrical domain. This model, without the resistance represented for f(u), is a linearization of Kirchhoff's equation for small vibrations of a stretched elastic string when the ends are variables, see Medeiros, Limaco, Menezes (2002). We employ a variant, due to Zuazua (1990b), of the Hilbert Uniqueness Method (HUM), idealized by Lions (1988a, b).
Źródło:
Control and Cybernetics; 2004, 33, 2; 237-257
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonoverlapping domain decomposition for optimal control problems governed by semilinear models for gas flow in networks
Autorzy:
Leugering, G.
Martin, A.
Schmidt, M.
Sirvent, M.
Powiązania:
https://bibliotekanauki.pl/articles/205527.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
gas networks
Euler equation
semilinear PDE
nonoverlapping domain decomposition
Opis:
We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs—ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.
Źródło:
Control and Cybernetics; 2017, 46, 3; 191-225
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal sparse boundary control for a semilinear parabolic equation with mixed control-state constraints
Autorzy:
Casas, Eduardo
Troltzsch, Fredi
Powiązania:
https://bibliotekanauki.pl/articles/970122.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
semilinear parabolic equation
optimal control
sparse boundary control
mixed control-state constraints
Opis:
A problem of sparse optimal boundary control for a semilinear parabolic partial differential equation is considered, where pointwise bounds on the control and mixed pointwise control-state constraints are given. A standard quadratic objective functional is to be minimized that includes a Tikhonov regularization term and the L1-norm of the control accounting for the sparsity. Applying a recent linearization theorem, we derive first-order necessary optimality conditions in terms of a variational inequality under linearized mixed control state constraints. Based on this preliminary result, a Lagrange multiplier rule with bounded and measurable multipliers is derived and sparsity results on the optimal control are demonstrated.
Źródło:
Control and Cybernetics; 2019, 48, 1; 89-124
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Constrained controllability of second order dynami cal systems with delay
Autorzy:
Klamka, J.
Powiązania:
https://bibliotekanauki.pl/articles/205540.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
controllability
second-order dynamical systems
delayed control systems
semilinear control systems
constrained controls
Opis:
The paper considers finite-dimensional dynami cal control systems described by second order semilinear stationary ordinary differential state equations with delay in control. Using a generalized open mapping theorem, sufficient conditions for constrained local controllability in a given time interval are formulated and proved. These conditions require verification of constrained global controllability of the associated linear first-order dynamical control system. It is generally assumed that the values of admissible controls are in a convex and closed cone with vertex at zero. Moreover, several remarks and comments on the existing results for controllability of semilinear dynamical control systems are also presented. Finally, a simple numerical example which illustrates theoretical considerations is also given. It should be pointed out that the results given in the paper extend for the case of semilinear second-order dynamical systems constrained controllability conditions, which were previously known only for linear second-order systems.
Źródło:
Control and Cybernetics; 2013, 42, 1; 111-121
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second-order optimality conditions for semilinear elliptic control problems with constraints on the gradient of the state
Autorzy:
Casas, E.
Fernandez, J.
Mateos, M.
Powiązania:
https://bibliotekanauki.pl/articles/206719.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
optimal control
second order conditions
semilinear elliptic PDE
state gradient constraints
Opis:
The aim of this paper is to state the second order necessary and sufficient optimality conditions for distributed control problems governed by the Neumann problem associated to a semilinear elliptic partial differential equation. Bound constraints ou control are considered, as well as equality and inequality constraints of integral type on the gradient of the state.
Źródło:
Control and Cybernetics; 1999, 28, 3; 463-479
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact penalization of pointwise constraints for optimal control problems
Autorzy:
Casas, E.
Powiązania:
https://bibliotekanauki.pl/articles/970884.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
semilinear elliptic equations
pointwise state constraints
exact penalization
first and second order optimality conditions
Opis:
In this paper we consider a control problem governed by a semilinear elliptic equation with pointwise control and state constraints. We analyze the existence of an exact penalization of the state constraints. In particular, we prove that the first and second order optimality conditions imply the existence of such a penalization. Finally, we prove some extra regularity of the strict local minima of the control problem, assuming the existence of an exact penalization for them.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1131-1150
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints
Autorzy:
Neitzel, I.
Troltzsch, F.
Powiązania:
https://bibliotekanauki.pl/articles/970314.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
semilinear parabolic equation
pointwise state constraints
Moreau-Yosida regularization
Lavrentiev regularization
convergence
strong regularity
local uniqueness
Opis:
Moreau-Yosida and Lavrentiev type regularization methods are considered for nonlinear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to infinity or zero, respectively. In particular, the strong convergence of global and local solutions is addressed. Moreover, strong regularity of the Lavrentiev-regularized optimality system is shown under certain assumptions, which, in particular, allows to show that locally optimal solutions of the Lavrentiev regularized problems are locally unique. This analysis is based on a second-order sufficient optimality condition and a separation assumption on almost active sets.
Źródło:
Control and Cybernetics; 2008, 37, 4; 1013-1043
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
Tytuł:
Optimal control of semilinear evolution inclusions via discrete approximations
Autorzy:
Mordukhovich, B. S.
Wang, D.
Powiązania:
https://bibliotekanauki.pl/articles/1839178.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
analiza wariacyjna
różniczkowanie uogólnione
aproksymacja dyskretna
warunek konieczny optymalności
optimal control
variational analysis
generalized differentiation
semilinear evolution inclusions
discrete approximations
necessary optimality conditions
Opis:
This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for constrained continuous-time evolution inclusions by passing to the limit from discrete approximations.
Źródło:
Control and Cybernetics; 2005, 34, 3; 849-870
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:
Sequential optimization for semilinear divergent hyperbolic equation with a boundary control and state inequality constraint
Autorzy:
Gavrilov, V. S.
Sumin, M. I.
Powiązania:
https://bibliotekanauki.pl/articles/206311.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Radon measures
sequential optimization
maximum principle for minimizing sequences
semilinear hyperbolic partial differential equations
pointwise in time state constraints
boundary control
value function
sensitivity
normality
regularity
twoparameter needle variation of controls
Opis:
An optimal control problem with a state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind is considered. The state constraint contains a functional parameter that belongs to the class of continuous functions and occurs as an additive term. We study the properties of solutions of linear hyperbolic equations in divergence form with measures in the original data and compute the first variations of functionals on the basis of a so-called two-parameter needle variation of controls. We consider the necessary conditions for minimizing sequences in an optimal control problem with a pointwise in time state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind. For the parametric optimization problem, we also consider regularity and normality conditions stipulated by the differential properties of its value function.
Źródło:
Control and Cybernetics; 2014, 43, 2; 183-226
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 16

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