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Tytuł:
Higher-order conditions for local equilibria in a discontinuous Gale economic model
Autorzy:
Michalak, A.
Studniarski, M.
Powiązania:
https://bibliotekanauki.pl/articles/205957.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Gale model
equilibrium
higher-order conditions
generalized directional derivatives
Opis:
The paper introduces the concept of a strict local equilibrium of order k in the Gale economic model. We obtain higher-order necessary and sufficient conditions for such equilibria without assuming continuity of the utility functions. These conditions are formulated in terms of generalized lower and upper directional derivatives, introduced by Studniarski (1986). A stability theorem for strict local equilibria of order k is also included.
Źródło:
Control and Cybernetics; 2017, 46, 1; 37-47
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minima in control problems with constraints
Autorzy:
Stefani, Gianna
Zezza, PierLuigi
Powiązania:
https://bibliotekanauki.pl/articles/1359682.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
state-control constraint
necessary
second order conditions
conjugate points
optimal control
sufficient conditions
Opis:
This paper is devoted to describing second order conditions in the framework of extremal problems, that is, conditions obtained by reducing the optimal control problem to an abstract one in a suitable Banach (or Hilbert) space. The studied problem includes equality constraints both on the end-points and on the state-control trajectory. The second goal is to give a complete description of necessary and sufficient second order conditions for weak local optimality by describing first the associated linear-quadratic problem and then by giving a conjugate point theory for this linear quadratic problem with constraints.
Źródło:
Banach Center Publications; 1995, 32, 1; 361-378
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
Autorzy:
Auzinger, W.
Herfort, W.
Powiązania:
https://bibliotekanauki.pl/articles/255869.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
exponential splitting schemes
local error
defect
order conditions
free Lie algebra
Opis:
We discuss the structure of the local error of exponential operator splitting methods. In particular, it is shown that the leading error term is a Lie element, i.e., a linear combination of higher-degree commutators of the given operators. This structural assertion can be used to formulate a simple algorithm for the automatic generation of a minimal set of polynomial equations representing the order conditions, for the general case as well as in symmetric settings.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 243-256
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Necessary and sufficient conditions for a Pareto optimal allocation in a discontinuous Gale economic model
Autorzy:
Michalak, A.
Studniarski, M.
Powiązania:
https://bibliotekanauki.pl/articles/255729.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Gale model
discontinuous functions
generalized directional derivatives
higher-order conditions
Pareto optimality
Opis:
In this paper we examine the concept of Pareto optimality in a simplified Gale economic model without assuming continuity of the utility functions. We apply some existing results on higher-order optimality conditions to get necessary and sufficient conditions for a locally Pareto optimal allocation.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 827-835
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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:
On relations among the generalized second-order directional derivatives
Autorzy:
Pastor, Karel
Powiązania:
https://bibliotekanauki.pl/articles/729322.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized second-order directional derivative
convexity
second-order optimality conditions
Opis:
In the paper, we deal with the relations among several generalized second-order directional derivatives. The results partially solve the problem which of the second-order optimality conditions is more useful.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 235-247
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order conditions for periodic optimal control problems
Autorzy:
Allwright, J.
Vinter, R.
Powiązania:
https://bibliotekanauki.pl/articles/970564.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie Riccatiego
programowanie dynamiczne
second order conditions
periodic optimal control
Riccati equations
dynamic programming
Opis:
This paper concerns second order sufficient conditions of optimality, involving the Riccati equation, for optimal control problems with periodic boundary conditions. The problems considered involve no pathwise constraints and are 'regular', in the sense that the strengthened Legendre-Clebsch condition is assumed to be satisfied. A well-known sufficient, condition, which we refer to as the Riccati sufficient condition, requires the existence of a global solution to the Riccati equation whose endpoint values satisfy a certain inequality. A sharper condition, named the extended sufficient, condition, takes the form of an inequality involving the solutions of a Riccati equation and two additional linear matrix equations. We highlight the superiority of the extended Riccati sufficient condition and develop a number of equivalent formulations of this condition. Not only does the extended Riccati sufficient, condition supply more information about, minimizers, but it is the basis of simpler numerical tests for assessing whether an extremal is a minimizer, at least in a local sense. The Riccati and also the extended Riccati sufficient conditions are applied to a variant of Speyer's 'sailboat' problem, involving parameters. It is found that the extended Riccati sufficient condition identifies a much larger set of points on parameter space for which a nominal control is optimal, in comparison to the Riccati sufficient condition.
Źródło:
Control and Cybernetics; 2005, 34, 3; 617-643
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Revisiting the analysis of optimal control problems with several state constraints
Autorzy:
Bonnans, J. F.
Hermant, A.
Powiązania:
https://bibliotekanauki.pl/articles/970908.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
state constraints
shooting algorithm
second order optimality conditions
Opis:
This paper improves the results of and gives shorter proofs for the analysis of state constrained optimal control problems than presented by the authors in Bonnans and Hermant (2009b), concerning second order optimality conditions and the well-posedness of the shooting algorithm. The hypothesis for the second order necessary conditions is weaker, and the main results are obtained without reduction to the normal form used in that reference, and without analysis of high order regularity results for the control. In addition, we provide some numerical illustration. The essential tool is the use of the "alternative optimality system".
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1021-1052
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order optimality conditions for bang-bang control problems
Autorzy:
Maurer, H.
Osmolovskii, N. P.
Powiązania:
https://bibliotekanauki.pl/articles/970524.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie przekaźnikowe
bang-bang control
second order necessary and sufficient conditions
critical cone
transformation of quadratic forms
numerical verification of second order conditions
van der Pol oscillator
Opis:
Second order necessary and sufficient optimality conditions for bang-bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi-)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadratic form and the critical cone which will be tailored to different types of control problems in practice. In particular, by means of a solution to a linear matrix differential equation, the quadratic form can be converted to perfect squares. We demonstrate by three practical examples that the conditions obtained can be verified numerically.
Źródło:
Control and Cybernetics; 2003, 32, 3; 555-584
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient optimality conditions for a bang-singular extremal in the minimum time problem
Autorzy:
Poggiolini, L.
Stefani, G.
Powiązania:
https://bibliotekanauki.pl/articles/969613.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
minimum time
second order sufficient conditions
bang-singular arc
Hamiltonian formalism
Opis:
The paper gives second order sufficient conditions for the strong local optimality of a bang-singular extremal in a minimum time problem. The conditions are given in terms of regularity assumptions on the extremal and of the coercivity of the extended second variation associated to the minimum time problem with fixed end-points on the singular arc. The conditions are close to the necessary ones in the usual sense, namely we require strict inequalities where necessary conditions have mild inequalities.
Źródło:
Control and Cybernetics; 2008, 37, 2; 469-490
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:
Sensitivity analysis for optimal control of problems governed by semilinear parabolic equations
Autorzy:
Bergounioux, M.
Merabet, N.
Powiązania:
https://bibliotekanauki.pl/articles/206854.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
analiza czułości
sterowanie optymalne
optimal control
second order optimality conditions
sensitivity analysis
Opis:
We investigate an optimal control problem governed by a semilinear parabolic equation with perturbed initial data. We perform some sensitivity analysis: under polyhedricity assumption and second order optimality conditions we derive second order expansion of the optimal value function.
Źródło:
Control and Cybernetics; 2000, 29, 4; 861-886
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order sufficient conditions and sensitivity analysis for optimal multiprocess control problems
Autorzy:
Augustin, D.
Maurer, H.
Powiązania:
https://bibliotekanauki.pl/articles/206723.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
multiprocess control systems
Riccati equations
robot control
second order sufficient conditions
sensitivity analysis
Opis:
Second order sufficient optimality conditions (SSC) are derived for optimal multiprocess control problems. For that purpose the multiprocess control problem is transformed into a single stage control problem with augmented state variables which comprise the state variables of all individual stages as well as the switching times as choice variables. This toansformation allows to apply the known SSC for single stage control problems. A numerical test of SSC involves the solution of an associated Riccati equation together with boundary conditions adapted to the multiprocess. Sensitivity analysis of parametric multiprocess problems can be based on SSC. A numerical example of the optimal two-stage control of a robot illustrates both SSC and sensitivity analysis.
Źródło:
Control and Cybernetics; 2000, 29, 1; 11-31
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order convexity and a modified objective function method in mathematical programming
Autorzy:
Antczak, T.
Powiązania:
https://bibliotekanauki.pl/articles/969778.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
programowanie matematyczne
mathematical programming
second order modified objective function optimization problem
second order convex function
second order optimality conditions
Opis:
An approach to nonlinear constrained mathematical programming problems which makes use of a second order derivative is presented. By using a second order modified objective function method, a modified optimization problem associated with a primal mathematical programming problem is constructed. This auxiliary optimization problem involves a second order approximation of an objective function constituting the primal mathematical programming problem. The equivalence between the original mathematical programming problem and its associated modified optimization problem is established under second order convexity assumption. Several practical O.R. applications show that our method is efficient. Further, an iterative algorithm based on this approach for solving the considered nonlinear mathematical programming problem is given for the case when the functions constituting the problem are second order convex. The convergence theorems for the presented algorithm are established.
Źródło:
Control and Cybernetics; 2007, 36, 1; 161-182
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations
Autorzy:
Casas, E.
Dhamo, V.
Powiązania:
https://bibliotekanauki.pl/articles/206408.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
Neumann boundary control
quasi-linear elliptic equation
Pontryagin principle
second order optimality conditions
Opis:
First- and second-order optimality conditions are established for the boundary optimal control of quasilinear elliptic equations with pointwise constraints on the control. The theory is developed for Neumann controls in polygonal domains of dimension two. For the derivation of second-order sufficient optimality conditions, which is the main goal of this paper, the regularity of the solutions to the state equation and its linearization is studied in detail. Moreover, a Pontryagin principle is proved. The main difficulty in the analysis of these problems is the nonmonotone character of the state equation.
Źródło:
Control and Cybernetics; 2011, 40, 2; 457-490
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:
A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint
Autorzy:
Osmolovskii, Nikolai P.
Powiązania:
https://bibliotekanauki.pl/articles/2183496.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
critical cone
quadratic form
first order tangent
second order tangent
second order optimality conditions
weak local minimum
inequality control constraint
Pontryagin’s maximum principle
Opis:
This paper is devoted to a sufficient second-order condition for a weak local minimum in a simple optimal control problem with one control constraint G(u) ≤ 0, given by a C2-function. A similar second-order condition was obtained earlier by the author for a strong minimum in a much more general problem. In the present paper, we would like to take a narrower perspective than before and thus provide shorter and simpler proofs. In addition, the paper uses the first and second order tangents to the set U, defined by the inequality G(u) ≤ 0. The main difficulty of the proof, clearly shown in the paper, refers to the set, where the gradient Hu of the Hamiltonian is small, but the condition of quadratic growth of the Hamiltonian is satisfied. The paper can be valuable for self-explanation and provides a basis for extensions.
Źródło:
Control and Cybernetics; 2022, 51, 2; 151--169
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations
Autorzy:
Roubicek, T.
Troltzsch, F.
Powiązania:
https://bibliotekanauki.pl/articles/970527.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie strumieniem danych
stabilność Lipschitza
incompressible viscous fluids
flow control
first and second order optimality conditions
Lipschitz stability
Opis:
An optimal control problem with quadratic cost functional for the steady-state Navier-Stokes equations with no-slip boundary condition is considered. Lipschitz stability of locally optimal controls with respect to certain perturbations of both the cost functional and the equation is proved provided a second-order sufficient optimality condition holds. For a sufficiently small Reynolds number, even global Lipschitz stability of the unique optimal control is shown.
Źródło:
Control and Cybernetics; 2003, 32, 3; 683-705
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
C^11 vector optimization problems and Riemann derivatives
Autorzy:
Ginchev, I.
Guerraggio, A.
Rocca, M.
Powiązania:
https://bibliotekanauki.pl/articles/970359.pdf
Data publikacji:
2004
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optymalizacja wektorowa
pochodna kierunkowa typu Riemanna
warunek optymalności dwuwskaźnikowy
vector optimization
Riemann-type directional derivatives
second-order optimality conditions
Opis:
In this paper we introduce a generalized second-order Riemann-type derivative for C^1'1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that, these conditions are stronger than those obtained by means of the second-order subdinerential in Clarke sense considered in Guerraggio, Luc (2001) and also to some extent than those obtained in Guerraggio, Luc, Minh (2001).
Źródło:
Control and Cybernetics; 2004, 33, 2; 259-273
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:
Network optimality conditions
Autorzy:
Osmolovskii, Nikolai P.
Qian, Meizhi
Sokołowski, Jan
Powiązania:
https://bibliotekanauki.pl/articles/31343935.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
network
optimal control problem
weak local minimum
Pontryagin’s maximum principle
critical cone
quadratic form
second order optimality conditions
Riccati equation
Opis:
Optimality conditions for optimal control problems arising in network modeling are discussed. We confine ourselves to the steady state network models. Therefore, we consider only control systems described by ordinary differential equations. First, we derive optimality conditions for the nonlinear problem for a single beam. These conditions are formulated in terms of the local Pontryagin maximum principle and the matrix Riccati equation. Then, the optimality conditions for the control problem for networks posed on an arbitrary planar graph are discussed. This problem has a set of independent variables xi varying within their intervals [0, li], associated with the corresponding beams at network edges. The lengths li of intervals are not specified and must be determined. So, the optimization problem is non-standard, it is a combination of control and design of networks. However, using a linear change of the independent variables, it can be reduced to a standard one, and we show this. Two simple numerical examples for the single-beam problem are considered.
Źródło:
Control and Cybernetics; 2023, 52, 2; 129-180
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A study of MHD fluid with second order slip and thermal flow over a nonlinear stretching sheet
Autorzy:
Jauhri, Shefali
Mishra, Upendra
Powiązania:
https://bibliotekanauki.pl/articles/2174199.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
płyn magnetyczny
nanociecz
metoda Runge-Kutty
stagnation point flow
second order slip boundary conditions
nonlinear stretching sheet
Runge-Kutta method
Opis:
An electrically conducted viscous incompressible nanofluid flow caused by the nonlinear stretching surface with stagnation flow has been investigated numerically. The effect of Brownian motion and thermophoresis on the nanofluid is also incorporated. The governing partial differential equations with nonlinear second order boundary conditions are solved by the fourth order Runge-Kutta technique using MATLAB programming. The effect of the radiation parameter (Rd), stretching parameter (n), Brownian motion parameter (Nb), thermophoresis parameter (Nt) on temperature, velocity and mass transfer are shown graphically. The influence of some of these parameters on the local Nusselt number (−′(0)) and local Sherwood number (−′(0)) are shown by the graphs.
Źródło:
International Journal of Applied Mechanics and Engineering; 2022, 27, 2; 98--114
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extremals of the time optimal control problem for a material point moving along a straight line in the presence of friction and limitation on the velocity
Autorzy:
Osmolovskii, N. P.
Figura, A.
Kośka, M.
Wójtowicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/206453.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
material point
resistance forces
acceleration
deceleration
Pontryagin’s maximum principle
second order optimality conditions
optimal control
adjoint variable
state constraint
Stieltjes measure
singular arc
boundary arc
Opis:
This paper provides an analysis of the time optimal control problem for a material point moving along a straight line in the presence of strength of resistance to movement (friction) and subject to constraint on the velocity. The point is controlled by a limited traction or braking force. The analysis of the problem is based on the maximum principle for state constraints in the Dubovitskii-Milyutin form, see Dubovitskii and Milyutin (1965), and the necessary second-order optimality condition for bang-bang controls, see Milyutin and Osmolovskii (1998).
Źródło:
Control and Cybernetics; 2017, 46, 4; 305-324
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
System of production order verification in application to service of customer
Autorzy:
Saniuk, A.
Saniuk, S.
Powiązania:
https://bibliotekanauki.pl/articles/118055.pdf
Data publikacji:
2005
Wydawca:
Polskie Towarzystwo Promocji Wiedzy
Tematy:
production order
sufficient conditions
production cost
Opis:
In this paper the efficiency of the System of Production Order Verification in application to service of customer is examined. Its aim is to find out whether a given work order can be accepted to be processed in an enterprise and satisfy the customer’s requirements within constraints imposed by the enterprise configuration and the process of manufacturing of other products. The presented system is illustrated on an example.
Źródło:
Applied Computer Science; 2005, 1, 1; 133-140
1895-3735
Pojawia się w:
Applied Computer Science
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
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