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Wyświetlanie 1-15 z 339
Tytuł:
An iterative method for time optimal control of dynamic systems
Autorzy:
Kashiri, N.
Ghasemi, M. H.
Dardel, M.
Powiązania:
https://bibliotekanauki.pl/articles/229435.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
dynamic systems
optimal control
time optimal control
bounded control inputs
Opis:
An iterative method for time optimal control of a general type of dynamic systems is proposed, subject to limited control inputs. This method uses the indirect solution of open-loop optimal control problem. The necessary conditions for optimality are derived from Pontryagin's minimum principle and the obtained equations lead to a nonlinear two point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and in solving the resulted TPBVP, a simple iterative method based on solving the minimum energy solution is proposed. The method does not need finding the switching point so that the resulted TPBVP can be solved by usual algorithms such as shooting and collocation. Also, since the solution of TPBVPs is sensitive to initial guess, a short procedure for making the proper initial guess is introduced. To this end, the accuracy and efficiency of the proposed method is demonstrated using time optimal solution of some systems: harmonic oscillator, robotic arm, double spring-mass problem with coulomb friction and F-8 aircraft.
Źródło:
Archives of Control Sciences; 2011, 21, 1; 5-23
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A simple proof of the maximum principle with endpoint constraints
Autorzy:
Korytowski, A.
Powiązania:
https://bibliotekanauki.pl/articles/205969.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
maximum principle
Opis:
The paper presents a new, relatively simple proof of Pontryagin’s maximum principle for the canonical problem of optimal control, with equality and inequality constraints imposed on the trajectory endpoints. The proof combines together two ideas, which appeared separately in the earlier works: application of the Karush-John conditions for finite-dimensional problems, and using packages of needle variations.
Źródło:
Control and Cybernetics; 2014, 43, 1; 5-13
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal reorientation of spacecraft orbit
Autorzy:
Chelnokov, Yu. N.
Pankratov, I. A.
Sapunkov, Y. G.
Powiązania:
https://bibliotekanauki.pl/articles/229458.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
spacecraft
optimal control
quaternion
Opis:
The problem of optimal reorientation of the spacecraft orbit is considered. For solving the problem we used quaternion equations of motion written in rotating coordinate system. The use of quaternion variables makes this consideration more efficient. The problem of optimal control is solved on the basis of the maximum principle. An example of numerical solution of the problem is given.
Źródło:
Archives of Control Sciences; 2014, 24, 2; 119-128
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dirichlet control problems in smooth and nonsmooth convex plain domains
Autorzy:
Casas, E.
Mateos, M.
Powiązania:
https://bibliotekanauki.pl/articles/206194.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
boundary control
Dirichlet control
Opis:
In this paper we collect some results about boundary Dirichlet control problems governed by linear partial differential equations. Some differences are found between problems posed on polygonal domains or smooth domains. In polygonal domains some difficulties arise in the corners, where the optimal control is forced to take a value which is independent of the data of the problem. The use of some Sobolev norm of the control in the cost functional, as suggested in the specialized literature as an alternative to the L2 norm, allows to avoid this strange behavior. Here, we propose a new method to avoid this undesirable behavior of the optimal control, consisting in considering a discrete perturbation of the cost functional by using a finite number of controls concentrated around the corners. In curved domains, the numerical approximation of the problem requires the approximation of the domain Ω typically by a polygonal domain Ωh, this introduces some difficulties in comparing the continuous and the discrete controls because of their definition on different domains Γ and Γh, respectively. We complete the existing recent analysis of these problems by proving the error estimates for a full discretization of the control problem. Finally, some numerical results are provided to compare the different alternatives and to confirm the theoretical predictions.
Źródło:
Control and Cybernetics; 2011, 40, 4; 931-955
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Evolution of structure for direct control optimization
Autorzy:
Szymkat, Maciej
Korytowski, Adam
Powiązania:
https://bibliotekanauki.pl/articles/729426.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
optimal control
direct optimization methods
Opis:
The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and flat generations are described in detail and illustrated with computational examples.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 1; 165-193
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
From optimal control to non-cooperative differential games: a homotopy approach
Autorzy:
Bressan, A.
Powiązania:
https://bibliotekanauki.pl/articles/970911.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
non-cooperative differential games
Nash equilibrium solution
optimal feedback control
Opis:
We propose a new approach to the study of Nash equilibrium solutions to non-cooperative differential games. The original problem is embedded in a one-parameter family of differential games, where the parameter 0 ∈ [0,1] accounts for the strength of the second player. When 0 = 0, the second player adopts a myopic strategy and the game reduces to an optimal control problem for the first player. As 0 becomes strictly positive, Nash equilibrium solutions can be obtained by studying a bifurcation problem for the corresponding system of Hamilton-Jacobi equations.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1081-1106
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regularization and discretization of linear-quadratic control problems
Autorzy:
Alt, W.
Seydenschwanz, M.
Powiązania:
https://bibliotekanauki.pl/articles/206162.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
bang-bang control
regularization
discretization
Opis:
We analyze regularizations of a class of linear-quadratic optimal control problems with control appearing linearly. It is shown that if the optimal control is bang-bang or if a coercivity condition for the state variables is satisfied, the solutions are continuous functions of the regularization parameter. Combining error estimates for Euler discretizations of the regularized problems with those for the regularization error, we choose the regularization parameter in dependence of the meshsize to obtain optimal convergence rates for the discrete solutions. Numerical experiments confirm the theoretical findings.
Źródło:
Control and Cybernetics; 2011, 40, 4; 903-920
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An itae optimal sliding mode controller for systems with control signal and velocity limitations
Autorzy:
Pietrala, Mateusz
Leśniewski, Piotr
Bartoszewicz, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/2204689.pdf
Data publikacji:
2023
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
sliding mode control
optimal control
state constraints
Opis:
In this paper, a sliding mode controller, which can be applied for second-order systems, is designed. Robustness to external disturbances, finite regulation time and a good system’s behaviour are required for a sliding mode controller. In order to achieve the first two of these three goals, a non-linear, time-varying switching curve is introduced. The representative point (state vector) belongs to this line from the very beginning of the control process, which results in elimination of the reaching phase. The stable sliding motion along the switching curve is provided. Natural limitations such as control signal and system’s velocity constraints will be taken into account. In order to satisfy them, the sliding line parameters will be properly selected. However, a good dynamical behaviour of the system has to be provided. In order to achieve that, the integral time absolute error (ITAE) quality index will be introduced and minimised. The simulation example will verify theoretical considerations.
Źródło:
Acta Mechanica et Automatica; 2023, 17, 2; 230--238
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Curvature of optimal control: Deformation of scalar-input planar systems
Autorzy:
Kawski, M.
Maxwell, P. T.
Powiązania:
https://bibliotekanauki.pl/articles/969596.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
krzywizna
optimal control
curvature
Opis:
The Pontryagin Maximum Principle and high-order open-mapping theorems generalize elementary first-derivative tests to nonlinear optimal control. They provide necessary conditions for a trajectory-control-pair to be optimal, or sufficient conditions for local controllability. Sufficient conditions for optimality (and necessary conditions for nonlinear controllability) are harder to obtain. Like the Legendre-Clebsch condition, they generally take the form of tests for definiteness of second order derivatives. Recently, Agrachev introduced an attractive alternative by developing a notion of curvature of optimal control that generalizes classical Gauss (and Ricci) curvatures. This theory naturally applies to systems whose controls take values on a circle or sphere. In this article we present initial studies of how this notion of curvature provides insight into the limiting case when the circles become degenerate ellipses in the form of closed intervals. Of particular interest are well studied accessible, but uncontrollable, nonlinear systems, and systems that exhibit conjugate points, in which the control takes values in a closed interval u = (u1, u2) ∈ [-1,1] x {0} ⊆ R². We focus on systems that are well-known models for the analysis of small-time local controllability and time-optimal control.
Źródło:
Control and Cybernetics; 2008, 37, 2; 353-367
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pontryagin Maximum Principle for coupled slow and fast systems
Autorzy:
Artstein, Z.
Powiązania:
https://bibliotekanauki.pl/articles/970920.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
singular perturbations
maximum principle
Opis:
When slow and fast controlled dynamics are coupled, the variational limit, as the ratio of time scales grows, is best depicted as a trajectory in a probability measures space. The effective control is then an invariant measure on the fast state-control space. The paper presents the form of the Pontryagin Maximum Principle for this variational limit and examines its relation to the Maximum Principle of the perturbed system.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1003-1019
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Maximum Principle of optimal control: A history of ingenious ideas and missed opportunities
Autorzy:
Pesch, H. J.
Plail, M.
Powiązania:
https://bibliotekanauki.pl/articles/970918.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
history of optimal control
maximum principle
Opis:
On the occasion of (more than) 50 years of optimal control theory, this paper deals with the development of the maximum principle of optimal control during the early times of the Cold War, when mathematicians in the US and the USSR made every endeavor to solve minimum time interception problems, which later on became prototypes of the first optimal control problems. The paper is a short survey on the history of optimal control, a sequence of ingenious ideas and regrets of missed opportunities. The conclusions of the paper are extracted from the second author's monograph on the development of optimal control theory from its commencements until it became an independent discipline in mathematics. The present paper also includes secondary literature published thereafter.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 973-995
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal Control in a Model of Chemotherapy-induced Radiosensilisation
Optymalne sterowanie w modelu radiochemioterapii uwzględniającym uwrażliwienie
Autorzy:
Bajger, Piotr
Fujarewicz, Krzysztof
Świerniak, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/953411.pdf
Data publikacji:
2019
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
radiochemotherapy
optimal control
survival curves
radiosensilisation
Opis:
  In this work, we consider a simple mathematical model of radiochemotherapy which includes a term responsible for radiosensitization. We focus on finding theoretically optimal controls which maximise tumour cure probability for a finite, fixed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by the inclusion of the radiosensilization term. By means of numerical simulations, we show that optimal control offers a moderate increase in survival time over a sequential treatment. We then revisit in more detail a question of measuring the synergy between the therapies by means of isobolograms, a common experimental technique for measuring the additivity of two treatments.
Źródło:
Mathematica Applicanda; 2019, 47, 1
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of a Laboratory DC Servo Motor
Optymalne sterowanie laboratoryjnym serwomechanizmem z silnikiem prądu stałego
Autorzy:
Gorczyca, P.
Hajduk, K.
Kołek, K.
Powiązania:
https://bibliotekanauki.pl/articles/274587.pdf
Data publikacji:
2011
Wydawca:
Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
Tematy:
sterowanie optymalne
serwomechanizm
metoda MSE
sterowanie czasooptymalne
optimal control
DC servo
MSE method
time optimal control
Opis:
Position control of DC motor is discussed and two control problems are investigated: first, time optimal and second, optimal in the sense of a quadratic performance index. Simple mathematical models, linear and nonlinear, of the DC motor are introduced. In the presented approach, the nonlinear model contains only the nonlinearity of static characteristic. Controllers based on linear and nonlinear models are constructed for both control problems. For the nonlinear model optimal solutions are computed with the use of the MSE method. Comparison of results of real-time and simulation experiments are presented.
W pracy przedyskutowano dwa problemy sterowania pozycyjnego serwomechanizmem z silnikiem prądu stałego: problem czasooptymalny oraz sterowanie optymalne w sensie kwadratowego wskaźnika jakości. Przedstawiono proste modele matematyczne: liniowy i nieliniowy. W nieliniowym modelu uwzględniono jedynie nieliniową charakterystykę statyczną silnika. Dla obydwu problemów zaprojektowano regulatory wykorzystując modele liniowy i nieliniowy. Optymalne sterowanie dla modelu nieliniowego obliczono za pomocą metody MSE. Przedstawiono porównanie eksperymentów symulacyjnych i eksperymentów czasu rzeczywistego.
Źródło:
Pomiary Automatyka Robotyka; 2011, 15, 12; 129-134
1427-9126
Pojawia się w:
Pomiary Automatyka Robotyka
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stabilization of linear systems in random horizon via control
Autorzy:
Kozłowski, E.
Powiązania:
https://bibliotekanauki.pl/articles/206800.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
linear quadratic control
random horizon
stability
Opis:
The control problem with random horizon at finie number of events is investigated in this paper, where the general aim of control is the stabilization (in mean square sense) of linear system at minimum cost. This problem is reduced to the task of optima control with established finite horizon. Moreover, the differences between stabilization with fixed and random horizons are also given. To illustrate those differences a numerical example is included.
Źródło:
Control and Cybernetics; 2013, 42, 2; 527-541
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729292.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neutral differential equations
Banach spaces
optimal control
Opis:
In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 1; 89-109
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 339

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