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Tytuł:
On a degenerate Riccati equation
Autorzy:
Kesavan, S.
Raymond, J. P.
Powiązania:
https://bibliotekanauki.pl/articles/970756.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
algebraic Riccati equation
optimal control
parabolic systems
Opis:
In this paper, we study the existence of solutions to a degenerate algebraic Riccati equation associated to an optimal control problem with infinite time horizon. Under some assumptions on the control system, we can select a solution to this Riccati equation providing a feedback control law able to stabilize the system.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1393-1410
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergences Analysis from the Solution Function of the Riccati Fractional Differential Equation by Using Modified Homotopy Perturbation Method
Autorzy:
Sevira, Nurazizah M.
Rusyaman, Endang
Firdaniza, Firdaniza
Subiyanto, Subiyanto
Supian, Sudradjat
Powiązania:
https://bibliotekanauki.pl/articles/1059423.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Convergent
Differential Equation
Fractional
Modified Homotopy Perturbation Method
Riccati
Opis:
A Fractional differential equation is an equation that contains derivatives with an order of fractional numbers. Same with natural number order differential equations, this type of equation is divided into linear and nonlinear fractional differential equations. One of the equations that include nonlinear fractional differential equation is Riccati fractional differential equation (RFDE). Various methods have been applied to find solutions for fractional differential equations Riccati, one of them is the Modified Homotopy Perturbation Method (MHPM) which is a modification of the Homotopy Perturbation Method by Zaid Odibat and Shaher Momani. In this study, the MHPM was used to find solutions for fractional differential equations Riccati, which were then used to analyze the convergence of the function sequences of the solution. The result shows us that the order sequence of Riccati fractional differential equation which converges to a number causes the solution function sequence of Riccati fractional differential equation will converge to the function of the solution of Riccati fractional differential equation with the order of this number.
Źródło:
World Scientific News; 2019, 128, 2; 71-87
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Robust Control of Linear Stochastic Systems with Fully Observable State
Autorzy:
Poznyak, Alexander
Taksar, M.
Powiązania:
https://bibliotekanauki.pl/articles/1339291.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
robust control
Riccati equation
stochastic differential equations
stochastic control
Opis:
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.
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 1; 35-46
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On operators of transition in Krein spaces
Autorzy:
Grod, A.
Kuzhel, S.
Sudilovskaya, V.
Powiązania:
https://bibliotekanauki.pl/articles/255652.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Krein spaces
indefinite metrics
operator of transition
operator Riccati equation
Opis:
The paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix L. In this way, we complete the known result (see Theorem 5.2 in the paper of S. Albeverio, A. Motovilov, A. Skhalikov, Integral Equ. Oper. Theory 64 (2004), 455-486) and show the equivalence between the existence of a strong solution K (//K// < 1) of the Riccati equation and similarity of the J-self-adjoint operator L to a self-adjoint one.
Źródło:
Opuscula Mathematica; 2011, 31, 1; 49-59
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A direct approach to linear-quadratic stochastic control
Autorzy:
Duncan, T. E.
Pasik-Duncan, B.
Powiązania:
https://bibliotekanauki.pl/articles/255863.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
linear-quadratic Gaussian control
Riccati equation for optimization
stochastic control
Opis:
A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.
Źródło:
Opuscula Mathematica; 2017, 37, 6; 821-827
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite-time SDRE control of F16 aircraft dynamics
Autorzy:
Chodnicki, Marcin
Pietruszewski, Paweł
Wesołowski, Mariusz
Stępień, Sławomir
Powiązania:
https://bibliotekanauki.pl/articles/2175113.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
aircraft modelling
state-dependent Riccati equations
finite-time optimal control
Opis:
This paper proposes a finite-time horizon suboptimal control strategy based on state-dependent Riccati equation (SDRE) to control of F16 multirole aircraft. Flight stabilizer control of super maneuverable aircraft is modelled and simulated. For aircraft modelling purpose a full 6 DOF model is considered and described by nonlinear state-space approach. Also a stable state-dependent parametrization (SDP) necessary for solution of the SDRE control problem is proposed. Solution of the SDRE control problem with adequate defined weighting matrices in performance index shows possibility of fast and optimal aircraft control in finite-time. The method in this form can be used for stabilization of aircraft flight and aerodynamics.
Źródło:
Archives of Control Sciences; 2022, 32, 3; 557--576
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Determination of optimal controllers. Comparison of two methods for electric network chain
Autorzy:
Górecki, H.
Zaczyk, M.
Powiązania:
https://bibliotekanauki.pl/articles/199967.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
filtr Kalmana
równanie Riccatiego
optimal controllers
Kalman equation
Riccati equation
Opis:
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.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 3; 267-273
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Uniqueness of the Riccati operator of the non-standard ARE of a third order dynamics with boundary control
Autorzy:
Lasiecka, Irena
Triggiani, Roberto
Powiązania:
https://bibliotekanauki.pl/articles/2183492.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
uniqueness
non-standard algebraic Riccati equation
Moore-Gibson-Thompson equation
Opis:
TheMoore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Algebraic Riccati Equation. The paper by Lasiecka and Triggiani (2022) recently contributed a comprehensive study of the Optimal Control Problem for the MGT-third order dynamics with boundary control, over an infinite time-horizon. A critical missing point in such a study is the issue of uniqueness (within a specific class) of the corresponding highly non-standard Algebraic Riccati Equation. The present note resolves this problem in the positive, thus completing the study of Lasiecka and Triggiani (2022) with the final goal of having on line feedback control, which is also optimal.
Źródło:
Control and Cybernetics; 2022, 51, 2; 171--189
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Bolza optimal synthesis problem for singular estimate control systems
Autorzy:
Lasiecka, I.
Tuffaha, A.
Powiązania:
https://bibliotekanauki.pl/articles/970760.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Bolza problem
Riccati equation
singular estimate control systems
fluid-structure interaction
Opis:
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.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1429-1460
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optical solitons in birefringent fibers with parabolic law nonlinearity
Autorzy:
Zhou, Q.
Zhu, Q.
Biswas, A.
Powiązania:
https://bibliotekanauki.pl/articles/174318.pdf
Data publikacji:
2014
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
solitons
parabolic law nonlinearity
birefringent fibers
Jacobian elliptic equation
Riccati
equation
Opis:
This paper studies the propagation of optical solitons through birefringent fibers with parabolic law nonlinearity. The Hamiltonian perturbations that are inter-modal dispersion, self-steepening, third-order dispersion and nonlinear dispersions are taken into account. Both, Riccati equation expansion method and Jacobian elliptic equation expansion method are used. Finally, analytical solutions that are Jacobian elliptic periodic traveling wave solutions, periodic solutions, unbounded solutions, singular solutions, bright and dark soliton solutions are obtained under several constraint conditions.
Źródło:
Optica Applicata; 2014, 44, 3; 399-409
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations
Autorzy:
Ishibashi, Kazuki
Powiązania:
https://bibliotekanauki.pl/articles/29519191.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nonoscillation
proportional derivative controller
Riccati technique
Mathieu equation
Whittaker-Hill equation
Opis:
The proportional derivative (PD) controller of a differential operator is commonly referred to as the conformable derivative. In this paper, we derive a nonoscillation theorem for damped linear differential equations with a differential operator using the conformable derivative of control theory. The proof of the nonoscillation theorem utilizes the Riccati inequality corresponding to the equation considered. The provided nonoscillation theorem gives the nonoscillatory condition for a damped Euler-type differential equation with a PD controller. Moreover, the nonoscillation of the equation with a PD controller that can generalize Whittaker-Hill-type equations is also considered in this paper. The Whittaker-Hill-type equation considered in this study also includes the Mathieu-type equation. As a subtopic of this work, we consider the nonoscillation of Mathieu-type equations with a PD controller while making full use of numerical simulations.
Źródło:
Opuscula Mathematica; 2023, 43, 1; 67-79
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The simulations of sequential of estimators for objects with a serial structure
Autorzy:
Kwater, T.
Krutys, P.
Powiązania:
https://bibliotekanauki.pl/articles/94851.pdf
Data publikacji:
2016
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Wydawnictwo Szkoły Głównej Gospodarstwa Wiejskiego w Warszawie
Tematy:
complex systems
dynamics equations
filter sequential
Riccati equation
bilinear equations
simulation
Opis:
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.
Źródło:
Information Systems in Management; 2016, 5, 3; 347-357
2084-5537
2544-1728
Pojawia się w:
Information Systems in Management
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Conditioning and error estimates in LQG design
Autorzy:
Petkov, P. Hr.
Konstantinov, M. M.
Christov, N. D.
Powiązania:
https://bibliotekanauki.pl/articles/971012.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
LQG control
Riccati equations
perturbation analysis
condition numbers
forward error estimation
Opis:
Efficient conditioning and error estimates are presented for the numerical solution of matrix Riccati equations in the continuous-time and discrete-time LQG design. The estimates implemented involve the solution of triangular Lyapunov equations along with usage of the LAPACK norm estimator.
Źródło:
Control and Cybernetics; 2008, 37, 1; 85-87
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear Optimal Tracking For Missile Gimbaled Seeker Using Finite-Horizon State Dependent Riccati Equation
Autorzy:
Khamis, A.
Naidu, D. S.
Kamel, A. M.
Powiązania:
https://bibliotekanauki.pl/articles/226218.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Finite-Horizon state dependent Riccati equation
nonlinear tracking
gimbaled missile seeker
Opis:
The majority of homing guided missiles use gimbaled seekers. The equations describing seeker gimbal system are highly nonlinear. Accurate nonlinear control of the motion of the gimbaled seeker through the attached DC motors is required. In this paper, an online technique for finite-horizon nonlinear tracking problems is presented. The idea of the proposed technique is the change of variables that converts the nonlinear differential Riccati equation to a linear Lyapunov differential equation. The proposed technique is effective for wide range of operating points. Simulation results for a realistic gimbaled system with different engagement scenarios are given to illustrate the effectiveness of the proposed technique.
Źródło:
International Journal of Electronics and Telecommunications; 2014, 60, 2; 165-171
2300-1933
Pojawia się w:
International Journal of Electronics and Telecommunications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences
Autorzy:
Schmeidel, E.
Powiązania:
https://bibliotekanauki.pl/articles/255806.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
linear
nonlinear
difference equations
third order
oscillatory solution
quasidifferences
Riccati technique
Opis:
In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 361-369
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Computer methods for calculating tuple solutions of polynomial matrix equations
Autorzy:
Dorożyński, J.
Nedashkovskyy, M.
Powiązania:
https://bibliotekanauki.pl/articles/200783.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
matrix polynomial equations
discrete (time) Riccati equation
tuples of solutions
MATLAB
Opis:
Schemes are presented for calculating tuples of solutions of matrix polynomial equations using continued fractions. Despite the fact that the simplest matrix equations were solved in the second half of the 19th century, and the problem of multiplier decomposition was then deeply analysed, many tasks in this area have not yet been solved. Therefore, the construction of computer schemes for calculating the sequences of solutions is proposed in this work. The second-order matrix equations can be solved by a matrix chain function or iterative method. The results of the numerical experiment using the MatLab package for a given number of iterations are presented. A similar calculation is done for a symmetric square matrix equation of the 2nd order. Also, for the discrete (time) Riccati equation, as its analytical solution cannot be performed yet, we propose constructing its own special scheme of development of the solution in the matrix continued fraction. Next, matrix equations of the n-th order, matrix polynomial equations of the order of non-canonical form, and finally, the conditions for the termination of the iterative process in solving matrix equations by branched continued fractions and the criteria of convergence of matrix branching chain fractions to solutions are discussed.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 2; 235-243
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A remark on the linearization technique in half-linear oscillation theory
Autorzy:
Dosly, O.
Powiązania:
https://bibliotekanauki.pl/articles/255798.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
half-linear oscillation theory
oscillation and nonoscillation criteria
Riccati technique
perturbation principle
Opis:
We show that oscillatory properties of the half-linear second order differential equation (r(t)Φ(x'))' + c(t)Φ(x) = 0, Φ(x) = |x|p-2x, p > 1, can be investigated via oscillatory properties of a certain associated second order linear differential equation. In contrast to paper [6], we do not need to distinguish between the cases p ≥ 2 and p ∈ (1, 2]. Our results also improve the oscillation and nonoscillation criteria given in [4].
Źródło:
Opuscula Mathematica; 2006, 26, 2; 305-315
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Delay-dependent Asymptotic Stabilitzation for Uncertain Time-delay Systems with Saturating Actuators
Autorzy:
Liu, P. L.
Powiązania:
https://bibliotekanauki.pl/articles/908496.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
stabilność
system opóźniania
równanie Riccatiego
stability
delay-dependency
time delay system
Riccati equation
Opis:
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.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2005, 15, 1; 45-51
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
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:
On the discrete time-varying JLQG problem
Autorzy:
Czornik, A.
Świerniak, A.
Powiązania:
https://bibliotekanauki.pl/articles/907993.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
automatyka
robotyka
jump linear systems
optimal control
time-varying systems
coupled Riccati equations
Opis:
In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2002, 12, 2; 203-207
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Suboptimal control of nonlinear continuous-time locally positive systems using input-state linearization and SDRE approach
Autorzy:
Bernat, J.
Kołota, J.
Stępień, S.
Superczyńska, P.
Powiązania:
https://bibliotekanauki.pl/articles/200111.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
positive nonlinear systems
feedback control
Riccati equation
sprzężenie zwrotne
układy nieliniowe
równanie Riccatiego
Opis:
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.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 1; 17-21
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
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:
On one oscillatory criterion for the second order linear ordinary differential equations
Autorzy:
Grigorian, G. A.
Powiązania:
https://bibliotekanauki.pl/articles/255069.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Riccati equation
normal and extremal solutions
integral and interval oscillatory criteria
generalized Hill's equation
Opis:
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.
Źródło:
Opuscula Mathematica; 2016, 36, 5; 589-601
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lyapunov, Sylvester and Riccati equations with some applications
Równania Lapunowa, Sylvestera i Riccatiego oraz ich niektóre zastosowania
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/157005.pdf
Data publikacji:
2007
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
algebraiczne
różniczkowe
równanie ,Lapunowa, Sylvestera, Riccatiego
algebraic
differential
equation, Lyapunov, Sylvester, Riccati
solution
application
Opis:
An overview of the differential and algebraic Lyapunov, Sylvester and Riccati equations is presented. A special attentions is focused on relationship between the equations and their applications in control systems theory. The well-known classical Cayley-Hammilton theorem is extended for the Lyapunov time-varying systems.
W pracy podano przegląd różniczkowych i algebraicznych równań Lapunowa, Sylvestera i Riccatiego. Szczególną uwagę zwrócono na związki występujące miedzy tymi równaniami oraz ich zastosowaniami w teorii sterowania i systemów. Uogólniono klasyczne twierdzenie Cayleya - Hamiltona na układy Lapunowa o zmiennych w czasie parametrach.
Źródło:
Pomiary Automatyka Kontrola; 2007, R. 53, nr 6, 6; 63-67
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Fast State-Space Algorithms for Predictive Control
Autorzy:
Błachuta, M. J.
Powiązania:
https://bibliotekanauki.pl/articles/908313.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
równanie różniczkowe Riccatiego
równanie Chandrasekhara
sterowanie predykcyjne
Riccati equation
Chandrasekhar equation
LQG control
predictive control
Opis:
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.
Źródło:
International Journal of Applied Mathematics and Computer Science; 1999, 9, 1; 149-160
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
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