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Wyświetlanie 1-15 z 41
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:
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:
Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
Autorzy:
Zabawa, T.S.
Powiązania:
https://bibliotekanauki.pl/articles/254967.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
stability of solutions
infinite systems
parabolic equations
elliptic equations
semilinear differential-functional equations
monotone iteration method
Opis:
A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as t → ∞ is the solution of the associated elliptic problem. The result is based on the monotone methods.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 173-183
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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
Tytuł:
Semilinear Functional Differential Equations of Fractional order with State-Dependent Delay
Autorzy:
Benchohra, Mouffak
Bennihi, Omar
Ezzinbi, Khalil
Powiązania:
https://bibliotekanauki.pl/articles/746657.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
semilinear functional differential equation, mild solution, resolvent family, fixed point, state-dependent delay, contractive map, Frechet space
Opis:
In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon-Granas type for contractions maps in Frechet spaces combined with \(\alpha\)-resolvent family is the main tool in our analysis.
Źródło:
Commentationes Mathematicae; 2013, 53, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Semilinear evolution equations of the parabolic type
Autorzy:
Bochenek, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1293838.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
classical solution
semilinear initial value problem
analytic semigroup
mild solution
Opis:
This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
Źródło:
Annales Polonici Mathematici; 1999, 72, 3; 197-206
0066-2216
Pojawia się w:
Annales Polonici Mathematici
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:
Second order semilinear Volterra integrodifferential equation in Banach space
Autorzy:
Bochenek, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1311971.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
cosine family
semilinear Volterra equation
Opis:
By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.
Źródło:
Annales Polonici Mathematici; 1992, 57, 3; 231-241
0066-2216
Pojawia się w:
Annales Polonici Mathematici
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:
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:
On the constrained and unconstrained controllability of semilinear Hilfer fractional systems
Autorzy:
Sikora, Beata
Powiązania:
https://bibliotekanauki.pl/articles/27312002.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
Hilfer fractional derivative
fractional systems
semilinear control systems
nonautonomous systems
Rothe's fixed point theorem
generalized Darbo fixed point theorem
Opis:
In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function f depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe’s fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.
Źródło:
Archives of Control Sciences; 2023, 33, 1; 155--178
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On periodic oscillations for a class of feedback control systems in Hilbert spaces
Autorzy:
Loi, Nguyen
Powiązania:
https://bibliotekanauki.pl/articles/729532.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
semilinear differential inclusion
periodic solution
guiding function
Opis:
In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions in Hilbert spaces we deal with the existence of periodic oscillations for a class of feedback control systems in Hilbert spaces.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 205-219
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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:
On controllability of second order dynamical systems – a survey
Autorzy:
Klamka, J.
Wyrwał, J.
Zawiski, R.
Powiązania:
https://bibliotekanauki.pl/articles/202359.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
exact controllability
approximate controllability
second-order dynamical systems
infinite dimensional systems
semilinear systems
sterowalność
układ nieskończenie wymiarowy
system półliniowy
Opis:
The paper presents a survey of recent results in the area of controllability of second order dynamical systems. Controllability problem for finite and infinite dimensional, linear, semilinear, deterministic and stochastic dynamical systems (with delays and undelayed) is taken into consideration. Different types of controllability are discussed.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 3; 279-295
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a semilinear elliptic eigenvalue problem
Autorzy:
Coclite, Mario
Powiązania:
https://bibliotekanauki.pl/articles/1294623.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
semilinear elliptic equations
nonlinear boundary-value problems
positive solutions
supersolution and subsolution method
Opis:
We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, $u|_{∂Ω} = 0$, where f(x) and h(u) satisfy minimal regularity assumptions.
Źródło:
Annales Polonici Mathematici; 1997, 67, 3; 289-295
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 41

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