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Wyświetlanie 1-15 z 21
Tytuł:
On the existence of Luenberger reduced order observer
Autorzy:
Kiritsis, Konstadinos H.
Powiązania:
https://bibliotekanauki.pl/articles/31343936.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Luenberger reduced order observer
necessary and sufficient conditions
Opis:
In this paper the explicit necessary and sufficient conditions for the existence of Luenberger reduced order observer are established. In particular, it is proven that for the given linear time-invariant system of order n, having p linearly independent out- puts and m inputs, a Luenberger observer of order (n − p) can be constructed if and only if the given system is detectable. Further- more, a procedure is given for the construction of the observer. Our approach is based on the properties of real and polynomial matrices.
Źródło:
Control and Cybernetics; 2023, 52, 2; 181-198
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Normality of the maximum principle for absolutely continuous solutions to Bolza problems under state constraints
Autorzy:
Frankowska, H.
Powiązania:
https://bibliotekanauki.pl/articles/970777.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
maximum principle under state constraints
normal necessary conditions
Opis:
It is well known that for a Bolza optimal control problem under state constraints every local minimizer satisfies a constrained maximum principle which may be degenerate. In the recent years several researchers proposed sufficient conditions for its nondegeneracy, e.g. Arutyanov and Assev (1997), Rampazzo and Vinter (1999, 2000), Galbraith and Vinter (2003). In all these papers the most important assumption links dynamics of a control system with tangent cones to constraints. It is the so called inward pointing condition of control theory that is in the same spirit with the well known Slater and Managasarian-Fromowitz conditions of mathematical programming. We propose here two sufficient conditions for normality when the boundary of constraints is C1 and the end point is free. The first one applies to every nondegenerate maximum principle without any assumptions on the initial state. The second one applies to every maximum principle, but involves an additional assumption on the initial conditions.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1327-1340
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Recent results on well-posedness and optimal control for a class of generalized fractional Cahn–Hilliard systems
Autorzy:
Colli, Pierluigi
Gilardi, Gianni
Sprekels, Jurgen
Powiązania:
https://bibliotekanauki.pl/articles/970119.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
fractional operators
Cahn-Hilliard system
optimal control
necessary optimality conditions
Opis:
In this paper, we give an overview of results for Cahn–Hilliard systems involving fractional operators that have recently been established by the authors of this note. We address problems concerning existence, uniqueness, and regularity of the solutions to the system equations, and we study optimal control problems for the systems. The well-posedness results are valid for a wide class of fractional operators of spectral type and for the typical double-well nonlinearities appearing in the Cahn–Hilliard system equations, namely the classical differentiable, the logarithmic, and the nondifferentiable double obstacle potentials. While this also applies to the existence of optimal controls in the related optimal control problems, the establishment of first-order necessary optimality conditions requires imposing much stronger assumptions on the admissible class of fractional operators. One main reason for this is the necessity of deriving suitable differentiability properties for the associated control-to-state mapping. Nevertheless, it turns out that also in the singular case of logarithmic potentials, the first-order necessary optimality conditions can be established under suitable assumptions, and a “deep quench” approximation, based on the results derived for logarithmic nonlinearities makes even the case of double obstacle potentials accessible.
Źródło:
Control and Cybernetics; 2019, 48, 1; 153-197
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On singular arcs in nonsmooth optimal control
Autorzy:
Oberle, H. J.
Rosendahl, R.
Powiązania:
https://bibliotekanauki.pl/articles/969559.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
nonsmooth optimal control problems
necessary conditions
singular state subarcs
Zermelo's problem
Opis:
In this paper we consider general optimal control problems (OCP) which are characterized by a nonsmooth ordinary state differential equation. However, we allow only mild types of nonsmoothness. More precisely, we assume that the right-hand side of the state equation is piecewise smooth and that the switching points, which separate these pieces, are determined as points, where a state-and possibly control-dependent (smooth) switching function changes sign. For this kind of optimal control problems necessary optimality conditions are developed. Attention is paid to the situation when the switching function vanishes identically along a nontrivial subarc. Such subarcs, which we call singular state subarcs, are investigated with respect to necessary conditions and to junction conditions. In extension to earlier results of the authors, Oberle and Rosendhal (2006), in this paper nonsmooth OCPs are considered with respect to the order of the switching function. Especially, the case of a zero-order switching function is included and examples of order zero, one and two are treated.
Źródło:
Control and Cybernetics; 2008, 37, 2; 429-450
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Variational principles for set-valued mappings with applications to multiobjective optimization
Autorzy:
Bao, T. Q.
Mordukhovich, B. S.
Powiązania:
https://bibliotekanauki.pl/articles/970283.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
multiobjective optimization
variational principles
generalized differentiation
necessary optimality and suboptimality conditions
Opis:
This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which-being certainly of independent interest-are mainly motivated by applications to multiobjective optimization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued extension of the subdifferential principle by Mordukhovich and Wang, formulated via an appropriate subdifferential notion for set-valued mappings with values in partially ordered spaces. Based on these variational principles and corresponding tools of generalized differentiation, we derive new conditions of the coercivity and Palais-Smale types ensuring the existence of optimal solutions to set-valued optimization problems with noncompact feasible sets in infinite dimensions and then obtain necessary optimality and suboptimality conditions for nonsmooth multiobjective optimization problems with general constraints, which are new in both finite-dimensional and infinite-dimensional settings.
Źródło:
Control and Cybernetics; 2007, 36, 3; 531-562
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extremals in the problem of minimum time obstacle avoidance for a 2D double integrator system
Autorzy:
Osmolovskii, N. P.
Figura, A.
Koska, M.
Wojtowicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/206001.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
necessary optimality condition
state constraint
optimal control
bang-bang control
Pontryagin principle
Opis:
This paper provides an analysis of time optimal control problem of motion of a material point in the plane outside the given circle, without friction. The point is controlled by a force whose absolute value is limited by one. The closure of exterior of the circle plays the role of the state constraint. The analysis of the problem is based on the minimum principle.
Źródło:
Control and Cybernetics; 2015, 44, 2; 185-209
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Necessary optimality conditions for nonsmooth two-dimensional control systems described by Roessers model
Autorzy:
Studniarski, M.
Powiązania:
https://bibliotekanauki.pl/articles/206015.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
generalized gradients
necessary conditions
optimal control
two-dimensional discrete systems
Opis:
Necessary optimality conditions for nonlinear nonsmooth two-dimensional discrete control systems are derived. Under additional convexity assumptions, these conditions can be obtained in the form of a maximum principle. For some special cases, sufficient optimality conditions are also presented.
Źródło:
Control and Cybernetics; 1998, 27, 1; 51-61
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Duality theory for state-constrained control problems governed by a first order PDE system
Autorzy:
Pickenhain, S.
Powiązania:
https://bibliotekanauki.pl/articles/205959.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
teoria dwoistości
control problems with multiple integrals
duality theory
necessary and sufficient optimality conditions
Opis:
In this paper we prove weak and strong duality results for optimal control problems with multiple integrals, first-order partial differential equations and state constraints. We formulate conditions under which the sequence of canonical variables [y^epsilon] in the [epsilon]-maximum principle, proved in Pickenhain and Wagner (2000), form a maximizing sequence in the dual problem.
Źródło:
Control and Cybernetics; 2002, 31, 3; 833-845
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control for a steady state dead oil isotherm problem
Autorzy:
Sidi Ammi, M. R.
Malinowska, A. B.
Torres, D. F. M.
Powiązania:
https://bibliotekanauki.pl/articles/205514.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
dead oil isotherm problem
optimal control
existence and regularity of solutions
necessary optimality conditions
Opis:
We study the optimal control of a steady-state dead oil isotherm problem. The problem is described by a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of mechanics of a continuous medium. Existence and regularity results of the optima control are proved, as well as necessary optimality conditions.
Źródło:
Control and Cybernetics; 2013, 42, 2; 459-470
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second-order necessary conditions of the Kuhn-Tucker type in multiobjective programming problems
Autorzy:
Aghezzaf, B.
Powiązania:
https://bibliotekanauki.pl/articles/970055.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
programowanie obiektowe
efficient solutions
multiobjective programming
second-order constraint qualification
second-order necessary conditions
Opis:
In this paper, we are concerned with a multiobjective programming problem with inequality constraints. We develop second-order necessary condition of the Kuhn-Tucker type for effciency and prove that the condition holds under a. constraint qualification. Moreover, we give some conditions which ensure that the constraint qua,lifica.tion holds.
Źródło:
Control and Cybernetics; 1999, 28, 2; 213-224
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On necessary conditions in variable end-time optimal control problems
Autorzy:
Ioffe, A.
Powiązania:
https://bibliotekanauki.pl/articles/970555.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
warunek konieczny optymalności
optimal control
necessary optimality condition
differential inclusion
variable end-time
Opis:
The paper contains a new necessary optimality condition for optimal control problems with free terminal time and discontinuous time dependence, which, actually is a family of conditions, each corresponding to a continuation of optimal trajectory beyond the optimal time for an arbitrary small interval.
Źródło:
Control and Cybernetics; 2005, 34, 3; 805-817
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order conditions in optimal control problems with mixed equality-type constraints on a variable time interval
Autorzy:
Osmolovskii, N. P.
Powiązania:
https://bibliotekanauki.pl/articles/970741.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
piecewise continuous control
maximum principle
second order necessary or sufficient conditions
critical cone
quadratic form
Opis:
This paper provides an analysis of second-order necessary or sufficient optimality conditions of Pontryagin or bounded strong minima, for optimal control problems of ordinary differential equations, considered on a nonfixed time interval, with constraints on initial-final time-state as well as mixed state-control constraints of equality type satisfying condition of linear independence of gradients w.r.t. control.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1535-1556
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The maximum principle in optimal control, then and now
Autorzy:
Clarke, F.
Powiązania:
https://bibliotekanauki.pl/articles/970551.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
warunek konieczny
zasada maksimum
analiza niegładka
optimal control
necessary conditions
maximum principle
nonsmooth analysis
Opis:
We discuss the evolution of the Pontryagin maximum principle, focusing primarily on the hypotheses required for its validity. We proceed to describe briefly a unifying result giving rise to both classical and new versions, a recent theorem of the author giving necessary conditions for optimal control problems formulated in terms of differential inclusions. We conclude with a new application of this result for the case in which mixed constraints on the state and control are imposed in terms of equalities, inequalities, and unilateral set constraints. In order to lighten the exposition, the discussion is limited to differentiable data, thereby avoiding mention of generalized gradients or normal cones, except, in the technical section on differential inclusions.
Źródło:
Control and Cybernetics; 2005, 34, 3; 709-722
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape optimization of thermoviscoelastic contact problems
Autorzy:
Myśliński, A.
Powiązania:
https://bibliotekanauki.pl/articles/970530.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optymalizacja kształtu
analiza czułości
warunek konieczny optymalności
dynamic thermoviscoelastic contact problem
shape optimization
sensitivity analysis
necessary optimality condition
Opis:
This paper is concerned with a shape optimization problem of a viscoelastic body in unilateral dynamic contact with a rigid foundation. The contact with Coulomb friction is assumed to occur at a portion of the boundary of the body. The nonpenetration condition is described in terms of velocities. The thermal deformation is taken into account. Using the material derivative method as well as the results concerning the regularity of solutions to dynamic variational thermoviscoelastic problem the directional derivative of the cost functional is calculated. A necessary optimality condition is formulated.
Źródło:
Control and Cybernetics; 2003, 32, 3; 611-627
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivalence of second order optimality conditions for bang-bang control problems. Part 1: Main results
Autorzy:
Osmolovskii, N. P.
Maurer, H.
Powiązania:
https://bibliotekanauki.pl/articles/970559.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie przekaźnikowe
stożek krytyczny
forma kwadratowa i równoważność
bang-bang control
second order necessary and sufficient conditions
critical cone
Opis:
Second order optimality conditions have been derived in the literature in two different forms. Osmolovskii (1988a, 1995, 2000, 2004) obtained second order necessary and sufficient conditions requiring that, a certain quadratic form be positive (semi)-definite on a critical cone. Agrachev, Stefani, Zezza (2002) first, reduced the bang-bang control problem to finite-dimensional optimization and then show that well-known sufficient optimality conditions for this optimization problem supplemented by the strict bang-bang property furnish sufficient conditions for the bang-bang control problem. In this paper, we establish the equivalence of both forms of sufficient conditions and give explicit relations between corresponding Lagrange multipliers and elements of critical cones. Part 1 summarizes the main results while detailed proofs will be given in Part 2.
Źródło:
Control and Cybernetics; 2005, 34, 3; 927-950
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 21

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