Wyniki wyszukiwania - Biblioteka Nauki

1

Różniczkowe równanie Riccatiego

100%

Langmann H.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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1998

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tom T. 2, z. 2

139--142

PL

W pracy zamieszczono procedurę rozwiązania różniczkowego równania Riccatiego. Przedstawiono transformację przekształcającą macierz Hamiltona do postaci blokowo-diagonalnej. Na tej podstawie uzyskano wzór analityczny przedstawiający rozwiązanie równania Riccatiego w funkcji rozwiązania algebraicznego równania Riccatiego.

EN

In the paper the analytical formula for the solution of the differential Riccati equation is presented.

2

Suboptimal control of nonlinear continuous-time locally positive systems using input-state linearization and SDRE approach

80%

Bernat J. , Kołota J. , Stępień S. , Superczyńska P.

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3

An algebraic approach to linear-quadratic optimization of second order dynamical systems

80%

Respondek J.

Archives of Control Sciences

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2007

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tom Vol. 17, no. 1

105-116

4

On one oscillatory criterion for the second order linear ordinary differential equations

80%

Grigorian G. A.

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tom Vol. 36, no. 5

589--601

EN

The Riccati equation method is used to establish an oscillatory criterion for second order linear ordinary differential equations. An oscillatory condition is obtained for the generalized Hill's equation. By means of examples the obtained result is compared with some known oscillatory criteria.

5

Robust Control of Linear Stochastic Systems with Fully Observable State

80%

Poznyak A. S. , Taksar M. I.

Applicationes Mathematicae

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1996-1997

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tom 24

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nr 1

35-46

EN

We consider a multidimensional linear system with additive inputs (control) and Brownian noise. There is a cost associated with each control. The aim is to minimize the cost. However, we work with the model in which the parameters of the system may change in time and in addition the exact form of these parameters is not known, only intervals within which they vary are given. In the situation where minimization of a functional over the class of admissible controls makes no sense since the value of such a functional is different for different systems within the class, we should deal not with a single problem but with a family of problems. The objective in such a setting is twofold. First, we intend to establish existence of a state feedback linear robust control which stabilizes any system within the class. Then among all robust controls we find the one which yields the lowest bound on the cost within the class of all systems under consideration. We give the answer in terms of a solution to a matrix Riccati equation and we present necessary and sufficient conditions for such a solution to exist. We also state a criterion when the obtained bound on the cost is sharp, that is, the control we construct is actually a solution to the minimax problem.

6

Determination of optimal controllers. Comparison of two methods for electric network chain

80%

Górecki H. , Zaczyk M.

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2018

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nr 3

7

Delay-dependent asymptotic stabilitzation for uncertain time-delay systems with saturating actuators

80%

Liu P.-L.

International Journal of Applied Mathematics and Computer Science

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2005

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tom 15

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nr 1

45-51

EN

This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.

8

Extended homogeneous balance conditions in the sub-equation method

80%

Song C. , Liu Y.

Journal of Applied Analysis

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2022

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tom Vol. 28, nr 1

165--179

EN

The sub-equation method is a kind of straightforward algebraic method to construct exact solutions of nonlinear evolution equations. In this paper, the sub-equation method is improved by proposing some extended homogeneous balance conditions. By applying them to several examples, it can be seen that new solutions could indeed be obtained.

9

A Bolza optimal synthesis problem for singular estimate control systems

80%

Lasiecka I. , Tuffaha A.

Control and Cybernetics

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2009

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tom Vol. 38, no 4B

1429-1460

EN

Bolza problem governed by PDE control systems with unbounded controls is considered. The motivating example is fluid structure interaction model with boundary-interface controls. The aim of the work is to provide optimal feedback synthesis associated with well denned gain operator constructed from the Riccati equation. The dynamics considered is of mixed parabolic-hyperbolic type which prevents applicability of tools developed earlier for analytic semigroups. It is shown, however, that the control operator along with the generator of the semigroup under consideration satisfy singular estimate referred to as Revisited Singular Estimate (RSE). This estimate, which measures "unboundedness" of control actions, is a generalization and a weaker form of Singular Estimate (SE) treated in the past literature. The main result of the paper provides Riccati theory developed for this new class of control systems labeled as RSECS (Revisited Singular Estimate Control Systems). The important feature is that the gain operator, constructed via Riccati operator, is consistent with the optimal feedback synthesis. The gain operator, though unbounded, has a controlled algebraically singularity at the terminal point. This enables one to establish well-posedness of the Riccati solutions and of the optimal feedback representation. An application of the theoretical framework to boundary control of a fluid-structure interaction model is given.

10

Zera i bieguny linii długiej RLCG ze sprzężeniami zwrotnymi Riccatiego

70%

Langmann H.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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1998

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tom T. 2, z. 2

143--147

PL

W pracy przedstawiono model matematyczny linii długiej objętej lokalnymi sprzężeniami zwrotnymi w każdym ogniwie. Dla takiego przypadku dokonano dekompozycji linii długiej na układy drugiego rzędu znajdując zera i bieguny transmisji analizowanego układu.

EN

In the paper the mathematical model of the network chain with local feedbacks in each element is presented. For this case is was made the decomposition of the network chain to the sum of second order system.

11

Determination of optimal controllers. Comparison of two methods for electric network chain

70%

Górecki H. , Zaczyk M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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tom Vol. 66, nr 3

267--273

EN

In the paper the comparison of two methods for calculation optimal gains is considered. One method using a Kalman procedure and one using a Riccati equation are compared. It is proved that a Kalman procedure is much better.

12

LQR and predictive control tuned via BDU

70%

Ramos C. , Sanchis J. , Martinez M. , Herrero J. M.

Systems Science

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2005

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tom Vol. 31, no 1

15-25

EN

This work presents the BDU technique (Bounded Data Uncertainties) and the tuning of the linear quadratic regulator (LQR) via this technique, which considers models with bounded uncertainties. The BDU method is based on constrained game-type formulations, and allows the designer to explicitly incorporate a priori information about bounds on the sizes of the uncertainties into the problem statement. Thus, on the one hand, the uncertainty effect is not over-emphasized, avoiding an overly conservative design and, on the other hand, the uncertainty effect is not under-emphasized, avoiding an overly sensitive to errors design. A feature of this technique consists of its geometric interpretation. The structure of the paper is the following, in the first section, some problems about the least-squares method in the presence of uncertainty are introduced. The BDU technique is shown in the second section and the LQR controller in the third. After that a new guided way of tuning the LQR is offered, taking into account the uncertainties bounds via the BDU. The consequence of this method is that both recursive and algebraic Riccati equations are modified. Finally, some examples are shown and the main conclusions and future work are commented.

13

Suboptimal control of nonlinear continuous-time locally positive systems using input-state linearization and SDRE approach

60%

Bernat J. , Kołota J. , Stępień S. , Superczyńska P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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tom Vol. 66, nr 1

17--21

EN

The infinite time suboptimal control problem for continuous-time nonlinear positive systems is formulated and solved. A solution to the problem using input-state linearization and state-dependent Riccati equation method (SDRE) is established, a procedure for solving the problem is proposed and illustrated with a numerical example.

14

THE SIMULATIONS OF SEQUENTIAL OF ESTIMATORS FOR OBJECTS WITH A SERIAL STRUCTURE

60%

Kwater T. , Krutys P.

Information Systems in Management

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2016

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tom 5

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nr 3

347-357

EN

The paper concerns the results of simulation of a certain approach, in which es-timation of object state associated with the decentralization of calculations. It is realized by dividing the optimization problem into sub-problems of smaller dimensionality. The main idea of the method is to assign individual quality indicators to each sub-object and to carry out the synthesis of estimators in a sequential manner, start-ing with the last sub-object. Implementation of the estimation process requires knowledge about the measurements of the individual sub-objects. The parameters of the filter sequential gains are calculated based on Riccati equation solutions for sub-objects and certain bilinear equations for cross-linkage connections. In the simulation tests the influence of types of connection between the sub-objects, the intensity disturbances of measurements and system on the values of coefficients of gains, as well as the estimation errors is presented.

15

On Fast State-Space Algorithms for Predictive Control

60%

Błachuta M. J.

International Journal of Applied Mathematics and Computer Science

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1999

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tom Vol. 9, no 1

149-160

EN

A Riccati-equation-based solution to a class of receding-horizon predictive control problems for an explicit-delay state-space model of an ARMAX system is found and the corresponding vector Chandrasekhar-type equations are derived for both filter and controller gains to improve the computational efficiency.

16

Adaptive control of continuous time linear stochastic system with quadratic cost functional

60%

Czornik A.

Matematyka Stosowana : matematyka dla społeczeństwa

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1996

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tom Nr 39

17--40

EN

An adaptive control problem for linear, continuous time stochastic system is described and solved in this paper. The unknown parameters in the model appear affinely in the drift term of the stochastic differential equation. The parameter estimates given by the maximum likelihood method are used to define the feedback gain. It is proved that the parameter estimates are strongly consistent and the cost functional reaches its minimum, i.e. the adaptive control is optimal. In this paper the continuity of the solution of the algebraic Riccati equation as a function of coefficient is also verified. The continuity is important for applications to problems in adaptive control.

PL

Praca składa się z czterech części. W części pierwszej sformułowano i podano rozwiązanie zagadnienia sterowania optymalnego w liniowym układzie stochastycznym z kwadratowym funkcjonałem kosztów na skończonym i nieskończonym przedziale czasowym. Twierdzenie 1, podające postać sterowania optymalnego na skończonym przedziale czasowym, jest dobrze znane ([l], [5]), natomiast twierdzenie 2 jest uogólnieniem znanych rezultatów. Zwykle formułuje się je przy założeniach gwarantujących istnienie i jedyność rozwiązania algebraicznego równania Riccatiego ([5], [4]). W tym sformułowaniu w jakim znajduje się w pracy można je znaleźć w [16] ale dla układu deterministycznego. W części drugiej zbadano własności algebraicznego równania Riccatiego. Algebraiczne równanie Riccatiego odgrywa pierwszoplanową rolę w konstrukcji sterowania optymalnego i poświęcono mu wiele uwagi w pracach [2], [4], [13], [15], Twierdzenie 5 pokazuje na jakie trudności możemy natrafić w procedurze adaptacyjnego sterowania, gdy nieznane współczynniki równania Riccatiego będziemy zastępować ich ocenami. Problem ten obszerniej omówiono w [4] i [8]. Głównym wynikiem tej części pracy jest twierdzenie 6, które odgrywa zasadniczą rolę w konstrukcji i dowodzie optymalności sterowania adaptacyjnego. W części trzeciej skonstruowano ocenę największego prawdopodobieństwa dla macierzy liniowej transformacji stanu. Estymator ten pojawił się po raz pierwszy w zagadnieniu sterowania optymalnego w pracy [12]. Wreszcie w czwartej, głównej części pracy podano algorytm sterowania adaptacyjnego oraz dowód jego optymalności (twierdzenie 10). Podany algorytm i dowód jego optymalności są modyfikacją wyników podanych w [6] i [7], Obejmują one ogólniejsze przypadki niż w tych pracach, gdzie zakłada się znajomość domkniętego, spójnego i ograniczonego zbioru, do którego należy oceniany parametr, niemniej uzyskane rezultaty są jeszcze dalekie od analogicznych wyników uzyskanych w pracy [3] dla czasu dyskretnego.

17

Delay-dependent Asymptotic Stabilitzation for Uncertain Time-delay Systems with Saturating Actuators

60%

Liu P. L.

International Journal of Applied Mathematics and Computer Science

|

2005

|

tom Vol. 15, no 1

45-51

EN

This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.

18

The simulations of sequential of estimators for objects with a serial structure

60%

Kwater T. , Krutys P.

Information Systems in Management

|

2016

|

tom Vol. 5, No. 3

347--357

EN

The paper concerns the results of simulation of a certain approach, in which estimation of object state associated with the decentralization of calculations. It is realized by dividing the optimization problem into sub-problems of smaller dimensionality. The main idea of the method is to assign individual quality indicators to each sub-object and to carry out the synthesis of estimators in a sequential manner, starting with the last sub-object. Implementation of the estimation process requires knowledge about the measurements of the individual sub-objects. The parameters of the filter sequential gains are calculated based on Riccati equation solutions for subobjects and certain bilinear equations for cross-linkage connections. In the simulation tests the influence of types of connection between the sub-objects, the intensity disturbances of measurements and system on the values of coefficients of gains, as well as the estimation errors is presented.

19

THE APPLICATION OF NASH GAME FOR DETERMINE OF CONTROLLING MULTIDIMENSIONAL OBJECTS

60%

Kwater T.

Metody Ilościowe w Badaniach Ekonomicznych

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2013

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tom 14

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nr 1

317-324

EN

The article presents the approach of decentralization of calculations related to the synthesis of controlling through division of an optimalization problem into lesser dimensionality subproblems. Applied was differential Nash game for objects of serial structure. The main idea of the method is to assign individual functionals of quality to subobjects and conduct the synthesis of regulators in a sequential way, beginning with the first subobject. Thanks to the sequential structure of the object it is possible to obtain a solution by decentralized optimizations

20

Unified reinterpretation of blood-flow kinematics as experimentally obcervable by means of standard echocardiography in terms of Riccati differential equation

60%

Cwetsch A.

Bulletin of the Polish Academy of Sciences. Biological Sciences

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2001

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tom 49

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nr 2