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Wyświetlanie 1-15 z 16
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:
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 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 derivatives and sufficient optimality conditions for shape funetionals
Autorzy:
Eppler, K.
Powiązania:
https://bibliotekanauki.pl/articles/206712.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal shape design
second directional derivatives
sufficient optimality conditions
Opis:
For sorne heuristic approaches to boundary variation in shape optimization the computation of second derivatives of domain and boundary integral functionals, their symmetry and a comparison to the velocity field or material derivative method are discussed. Moreover, for these approaches the functionals are Frechet-differentiable in some sense, because at least a local embedding into a Banach space problem is possible. This allows the discussion of sufficient condition in terms of a coercivity assumption on the second Frechet-derivative. The theory is illustrated by a discussion of the famous Dido problem.
Źródło:
Control and Cybernetics; 2000, 29, 2; 485-511
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:
Theconjugate points sufficient conditions for an optimal control
Autorzy:
Szymanowska, A.
Powiązania:
https://bibliotekanauki.pl/articles/206818.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
pola ekstremali
problem Bolza
sterowanie optymalne
warunek wystarczający
field of extremals
generalized problem of Bolza
sufficient conditions
Opis:
The paper concerns an application of the idea of field theory and the concept of "concourse of flights" to the sufficient optimality conditions for the optimal control problems stated in terms of focal and conjugate points. The concept of concourse of flights was begun by Young (1969), and later extended by Nowakowski (1988). In the paper the definition of a focal and conjugate point of a field of extremals is given. Using these concepts, we prove that the existence of a field of extremals without conjugate points implies the existence of concourse of flights and consequently we obtain the second order sufficient conditions for the generalized problem of Bolza. Another approach to the concept of focal and conjugate points is given by Zeidan (1983, 1984).
Źródło:
Control and Cybernetics; 1998, 27, 3; 353-362
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape optimization of control problems described by wave equations
Autorzy:
Nowakowski, A.
Powiązania:
https://bibliotekanauki.pl/articles/970316.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sufficient optimality conditions
control with wave equation
shape optimization
dual dynamic programming
Opis:
The control problem with multidimensional integral functional under wave type constraints for control is considered. Next a type of deformation with control of the domain is described and then we define suitable shape functional. Having denned trajectory and control of deformation dual dynamic programming tools are applied to derive optimality condition for the shape functional with respect to that deformation.
Źródło:
Control and Cybernetics; 2008, 37, 4; 1045-1055
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
Tytuł:
Multiobjective variational programming under generalized (V, p)-B-type I functions
Autorzy:
Khazafi, K.
Rueda, N.
Enflo, P.
Powiązania:
https://bibliotekanauki.pl/articles/970961.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
multiobjective variational programming
efficient solution
proper efficient solution
generalized (V, p)-B-type I functions
sufficient conditions
mixed type duality rusults
Opis:
In this paper, we generalize the (V, p)-invexity denned for nonsmooth multiobjective fractional programming by Mishra, Rueda and Giorgi (2003) to variational programming problems by defining new classes of vector- valued functions called (V, p)-B-type I and generalized (V, p)-B-type I. Then we use these new classes to derive various sufficient optimality conditions and mixed type duality results.
Źródło:
Control and Cybernetics; 2009, 38, 2; 555-572
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:
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:
Equivalence of second order optimality conditions for bang-bang control problems. Part 2 : Proofs, variational derivatives and representations
Autorzy:
Osmolovskii, N. P.
Maurer, H.
Powiązania:
https://bibliotekanauki.pl/articles/969736.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
bang-bang control
second order necessary and sufficient conditions
critical cones
equivalence of quadratic forms
representation of the Hessian of the Lagrangian
Opis:
In Part 1 of this paper (Osmolovskii and Maurer, 2005), we have summarized the main results on the equivalence of two quadratic forms from which second order necessary and sufficient conditions can be derived for optimal bang-bang control problems. Here, in Part 2, we give detailed proofs and elaborate explicit relations between Lagrange multipliers and elements of the critical cones in both approaches. The main analysis concerns the derivation of formulas for the first and second order derivatives of trajectories with respect to variations of switching times, initial and final time and initial point. This leads to explicit representations of the second order derivatives of the Lagrangian for the induced optimization problem. Based on a suitable transformation, we obtain the elements of the Hessian of the Lagrangian in a form which involves only first order variations of the nominal trajectory. Finally, a careful regrouping of all terms allows us to find the desired equivalence of the two quadratic forms.
Źródło:
Control and Cybernetics; 2007, 36, 1; 5-45
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient conditions and duality for multiobjective variational problems with generalized B-invexity
Autorzy:
Aghezzaf, B.
Khazafi, K.
Powiązania:
https://bibliotekanauki.pl/articles/970415.pdf
Data publikacji:
2004
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sufficient conditions
mixed type duality
multiobjective variational programming
efficient solution
B-type I vector-valued functions
generalized B-type I vector-valued functions
rozwiązanie efektywne
warunek wystarczający
Opis:
In this paper, we consider the multiobjective variational problem. We propose a class of generalized B-type I vector-valued functions and use this concept to establish sufficient optimality conditions and mixed type duality results
Źródło:
Control and Cybernetics; 2004, 33, 1; 113-126
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality conditions for state-constrained PDE control problems with time-dependent controls
Autorzy:
Los Reyes, J. C. de
Merino, P.
Rehberg, F.
Troltzsch, F.
Powiązania:
https://bibliotekanauki.pl/articles/971009.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie paraboliczne
równanie eliptyczne
sterowanie optymalne
parabolic equation
elliptic equation
optimal control
pointwise state constraints
sufficient optimality conditions
restricted control class
Opis:
The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are Rm -vector-valued functions of time, while they are vectors of Rm in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the extension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples are discussed that exhibit different forms of active sets and where second-order sufficient conditions are satisfied at the optimal solution.
Źródło:
Control and Cybernetics; 2008, 37, 1; 5-38
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dual sufficient optimality conditions for optimal control
Autorzy:
Młynarska, E.
Powiązania:
https://bibliotekanauki.pl/articles/205961.pdf
Data publikacji:
2001
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
minimum względne
nierówność podwójna Hamiltona-Jacobiego
zagadnienie sterowania optymalnego
dual Hamilton-Jacobi inequality
dual sufficient optimality conditions
optimal control problem
relative minimum
Opis:
In this paper we develop the first and second order dual sufficient optimality conditions for a nonlinear optimal control problem. Our conditions are derived from the dual Hamilton-Jacobi approach applied to the generalized problem of Bolza. We do not require neither any convexity on the data, nor that the control set U be polyhedral, nor that the control function be in the interior of U. Instead, we assume the existence of a function which satisfies a certain inequality.
Źródło:
Control and Cybernetics; 2001, 30, 1; 45-54
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 16

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