Citations with the tag: RICCATI equation
Results 51 - 100
- Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations.
GLIZER, V. Y. // IMA Journal of Mathematical Control & Information; Dec2007, Vol. 24 Issue 4, p435
An infinite horizon linear-quadratic optimal control problem for a singularly perturbed system with multiple point-wise and distributed small delays in the state variable is considered. The set of Riccati-type equations, associated with this problem by the control optimality conditions, is...
- Perturbation transfer matrix method for eigendata of one-dimensional structural system with parameter uncertainties.
Liu Bao-guo; Yin Xue-gang; Jian Kai-lin; Wu Yong // Applied Mathematics & Mechanics; Jul2003, Vol. 24 Issue 7, p801
A general method based on Riccati transfer matrix is presented to calculate the 2nd order perturbations of eigendatas for one-dimensional structural system with parameter uncertainties. The method is applicable to both real and complex eigendatas of any onedimensional structural system. The...
- Asymptotic Analysis and Solution of a Finite-Horizon H8 Control Problem for Singularly-Perturbed Linear Systems with Small State Delay.
Glizer, V.Y. // Journal of Optimization Theory & Applications; May2003, Vol. 117 Issue 2, p295
Analyzes a finite-Horizon control problem for singularly-perturbed linear systems with small state delay. Proposal of two approaches to the asymptotic analysis and solution of the problem; Construction of an asymptotic solution of the singularly-perturbed system of functional differential...
- Robust Equilibria in Indefinite Linear-Quadratic Differential Games.
van den Broek, W.A.; Engwerda, J.C.; Schumacher, J.M. // Journal of Optimization Theory & Applications; Dec2003, Vol. 119 Issue 3, p565
Equilibria in dynamic games are formulated often under the assumption that the players have full knowledge of the dynamics to which they are subject. Here, we formulate equilibria in which players are looking for robustness and take model uncertainty explicitly into account in their decisions....
- Special cases in a control problem.
Larin, V. // International Applied Mechanics; Feb2006, Vol. 42 Issue 2, p221
A number of control problems for mechanical systems with feedback are reduced to a matrix algebraic Riccati equation. The exact solutions of matrix algebraic Riccati equations with singularities are presented. These singularities do not permit the use of standard solution procedures. Asymptotic...
- Influence of shear strains on damping the vibrations of a rectangular plate with piezoelectric actuators.
Karnaukhov, V. G.; Tkachenko, Ya. V. // International Applied Mechanics; Dec2009, Vol. 45 Issue 12, p1365
The problem of active damping of the nonstationary vibrations of a hinged rectangular plate with distributed piezoelectric actuators is solved using Timoshenkoï¿½s hypotheses. To this end, two methods are employed: (i) a classical method of balancing the principal vibration modes by applying...
- Precise Solution of the Algebraic Riccati Equation for One-Input Relaxation Systems.
Borukhov, V. T.; Zelenyak, D. M. // Automation & Remote Control; Apr2003, Vol. 64 Issue 4, p531
Consideration was given to a special class of the algebraic Riccati equations arising in the theory of one-input relaxation systems. The precise solution obtained was used for rational parametrization of the dissipative manifold and the boundary of the set of solutions of the dissipative inequality.
- Mixed potentials in radiative stellar collapse.
Thirukkanesh, S.; Maharaj, S. D. // Journal of Mathematical Physics; Jul2010, Vol. 51 Issue 7, p072502
We study the behavior of a radiating star when the interior expanding, shearing fluid particles are traveling in geodesic motion. We demonstrate that it is possible to obtain new classes of exact solutions in terms of elementary functions without assuming a separable form for the gravitational...
- Design of dynamic suboptimal low-order controllers on basis of the H8-criterion.
Sadomtsev, Yu. // Automation & Remote Control; Dec2006, Vol. 67 Issue 12, p2021
A design problem of dynamic reduced-dimension controllers according to the boundedness condition of the H8-norm of a transfer matrix of a closed system is studied. The problem of controller deflation is related to the solution to degenerate filtering problems (no noise of measuring) and to...
- SENSITIVITY ANALISYS OF THE DISCRETE-TIME LMI-BASED H8 QUADRATIC STABILITY PROBLEM.
Yonchev, Andrey S.; Konstantinov, Mihail M.; Petkov, Petko H. // Proceedings of the International Conference on Information Techn; 2010, p245
The quadratic H8 control ensuring closed-loop performance y can be implicitly realized by the solutions Q, Y of a system of linear matrix inequalities (LMIs). The paper is concerned with performing linear sensitivity analysis for the discrete-time LMI based H quadratic stability problem, which...
- AN OPTIMAL CONSENSUS TRACKING CONTROL ALGORITHM FOR AUTONOMOUS UNDERWATER VEHICLES WITH DISTURBANCES.
Jian Yuan; Wen-Xia Zhang; Zhou-Hai Zhou // International Journal of Instrumentation & Control Systems; Apr2012, Vol. 2 Issue 2, p45
The optimal disturbance rejection control problem is considered for consensus tracking systems affected by external persistent disturbances and noise. Optimal estimated values of system states are obtained by recursive filtering for the multiple autonomous underwater vehicles modeled to...
- Soliton-like solutions and periodic form solutions for two variable-coefficient evolution equations using symbolic computation.
Li, B.; Chen, Y.; Zhang, H. Q. // Acta Mechanica; Jan2005, Vol. 174 Issue 1/2, p77
Some variable-coefficient generalizations of some nonlinear evolution equations (NLEEs) bear more realistic physical importance. By means of a generalized Riccati equation expansion (GREE) method and a symbolic computation system - Maple - we investigate the variable-coefficient Fisher-type...
- Oscillation of Second Order Neutral Differential Equations.
Yong Xia; Zhiting Xu // Southeast Asian Bulletin of Mathematics; 2006, Vol. 30 Issue 1, p157
Using the generalized Riccati technique and the averaging technique, new oscillation criteria for second order neutral differential equation [a(t)(x(t) - p(t)x(t - T))']' + q(t)f[x(t), x(t - s)]g[x'(t)] = 0 are obtained. These results extend and improve the oscillation criteria given by Ruan, Li...
- Sufficient Conditions for Stabilizability of Linear Periodic Differential Equations.
Phat, Vu Ngoc // Southeast Asian Bulletin of Mathematics; 2006, Vol. 30 Issue 2, p331
This paper studies a stabilizability problem for linear time-varying periodic differential equations. Based on the Floquet theory and discretization method, we give new sufficient conditions for stabilizability in terms of controllability rank condition of linear time-invariant discretized...
- The WKB method and differential consequences of the Riccati equation.
Chuprikov, N. L. // Mathematical Notes; Jun2011, Vol. 89 Issue 5/6, p885
generalized WKB method based on the use of the differential consequences of the Riccati equation is presented. The method combines the simplicity of the traditional WKB method and the universality of the Maslov method: in the case of a smooth potential with classical turning points in a bounded...
- Uniformly exponentially stable approximations for a class of second order evolution equations.
Karim Ramdani; Tak?o Takahashi; Marius Tucsnak // ESAIM: Control, Optimisation & Calculus of Variations; Jul2007, Vol. 13 Issue 3, p503
We consider the approximation of a class of exponentially stable infinite dimensional linear systems modelling the damped vibrations of one dimensional vibrating systems or of square plates. It is by now well known that the approximating systems obtained by usual finite element or finite...
- Traveling Wave Solutions and Soliton Solutions for A Generalized Burgers Equation with Variable Coefficients Using Symbolic Computation.
El-Boree, Mohammed Khalfallah // Journal of Modern Methods in Numerical Mathematics; 2011, Vol. 2 Issue 1/2, p45
We make use of the homogeneous balance method and symbolic computation to construct new exact traveling wave solutions for the generalized Burgers equation with variable coefficients. Many exact traveling wave solutions are successfully obtained, which contain soliton, soliton-like solutions,...
- A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS ON THE SPACE OF SYMMETRIC MATRICES.
Dragan, Vasile; Freiling, Gerhard; Hochhaus, Andreas; Morozan, Toader // Electronic Journal of Differential Equations; 2004, Vol. 2004, p1
In the first part of this paper we analyze the properties of the evolution operators of linear differential equations generating a positive evolution and provide a set of conditions which characterize the exponential stability of the zero solution, which extend the classical theory of Lyapunov....
- A GEOMETRIC APPROACH TO INTEGRABILITY CONDITIONS FOR RICCATI EQUATIONS.
Cari�ena, Jos� F.; De Lucas, Javier; Ramos, Arturo // Electronic Journal of Differential Equations; 2007, Vol. 2007, p1
Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.
- OSCILLATION OF SECOND-ORDER NONLINEAR IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES.
Mugen Huang; Weizhen Feng // Electronic Journal of Differential Equations; 2007, Vol. 2007, p1
In this article, we study the oscillation of second-order nonlinear impulsive dynamic equations on time scales. Using Riccati transformation techniques, we obtain sufficient conditions for oscillation of all solutions. An example is given to show that the impulses play a dominant part in...
- LINEAR UNCERTAIN NON-AUTONOMOUS TIME-DELAY SYSTEMS: STABILITY AND STABILIZABILITY VIA RICCATI EQUATIONS.
NIAMSUP, PIYAPONG; MUKDASAI, KANIT; PHAT, VU N. // Electronic Journal of Differential Equations; 2008, Vol. 2008, Special section p1
This paper addresses the problem of exponential stability for a class of uncertain linear non-autonomous time-delay systems. Here, the parameter uncertainties are time-varying and unknown but norm-bounded and the delays are time-varying. Based on combination of the Riccati equation approach and...
- Finding the strongly rank-minimizing solution to the linear matrix inequality.
Chaikovskii, M. M. // Automation & Remote Control; Sep2007, Vol. 68 Issue 9, p1559
Consideration is given to an nonstrict linear matrix inequality and associated Riccati equation that occurs on solving problems of analysis and synthesis of linear stationary discrete time systems. The strongly rank-minimizing solution to the considered linear matrix inequality also satisfies...
- Stabilization of linear autonomous systems of differential equations with distributed delay.
Dolgii, Yu. F. // Automation & Remote Control; Oct2007, Vol. 68 Issue 10, p1813
Consideration is given to the problem of optimal stabilization of differential equation systems with distributed delay. The optimal stabilizing control is formed according to the principle of feedback. The formulation of the problem in the functional space of states is used. It was shown that...
- Design of discrete H2-optimal reduced-order controllers.
Lutsenko, I.; Sadomtsev, Yu. // Automation & Remote Control; Oct2009, Vol. 70 Issue 10, p1698
Consideration was given to the design of discrete dynamic reduced-order controllers minimizing the H2-norm of the transfer matrix of a closed-loop system. The problem of reducing the controller order is related to the solution of the singular problem of filtration (no measurement noise) and...
- Transient Optical Regime of Two Level Atom in Laser Light.
Bougouffa, Smail; Al-Awfi, Saud // International Journal of Theoretical Physics; Apr2007, Vol. 46 Issue 4, p920
An extended analytic approach is considered for optical Bloch equations in the two level atom interacting with laser light. The separation approach of coupled differential equations is always possible with a sequence of special transformation into the Riccati nonlinear differential equation. The...
- OSCILLATION CRITERIA FOR SEMILINEAR ELLIPTIC EQUATIONS WITH A DAMPING TERM IN Rn.
TADIE // Electronic Journal of Differential Equations; 2010, Vol. 2010, Special section p1
We use a method based on Picone-type identities to find oscillation conditions for the equation n ? ij=1 ?/?xi (aij(x)?/?xj)u + f(x, u, ?u) + c(x)u = 0, with Dirichlet boundary conditions on bounded and unbounded domains. In this article, the above method substitudes the traditional Riccati...
- Constructive methods for obtaining the solution of the periodic boundary value problem for a system of matrix differential equations of Riccati type.
Laptinskii, V.; Rogolev, D. // Differential Equations; Oct2011, Vol. 47 Issue 10, p1426
In the nonsingular case, we obtain sufficient coefficient conditions for the unique solvability of the periodic boundary value problem for a system of matrix differential equations of Riccati type. We develop efficient algorithms for constructing the solution.
- On Algebraic Approach in Quadratic Systems.
Mencinger, Matej // International Journal of Mathematics & Mathematical Sciences; 2011, p1
When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and...
8-symmetries and nonlocal symmetries of exponential type.
MURIEL, C.; ROMERO, J. L. // IMA Journal of Applied Mathematics; Apr2007, Vol. 72 Issue 2, p191
Nonlocal symmetries generated by type I hidden symmetries are identified as specific
8-symmetries of an nth-order ordinary differential equation. The general method of reduction associated to these 8-symmetries allows us to give explicit transformations to reduce the order if n > 1....
- OSCILLATION CRITERIA FOR THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES.
TONGXING LI; ZHENLAI HAN; CHENGHUI ZHANG; YING SUN // Bulletin of Mathematical Analysis & Applications; Mar2011, Vol. 3 Issue 1, p52
By means of Riccati transformation technique, we establish some new oscillation criteria for the third-order nonlinear delay dynamic equations Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. on a time scale ? unbounded above, here ? > 0 is a quotient...
- New characterization of controllability via stabilizability and Riccati equation for LTV systems.
PHAT, V. N.; HA, Q. P. // IMA Journal of Mathematical Control & Information; Dec2008, Vol. 25 Issue 4, p419
This paper presents a new characterization of controllability via stabilizability and Riccati equation for linear time-varying systems. An equivalence is given between the global null controllability, complete stabilizability and the existence of the solution of some appropriate Riccati...
- Criteria for exponential stability of linear differential equations with positive evolution on ordered Banach spaces.
DRAGAN, VASILE; MOROZAN, TOADER // IMA Journal of Mathematical Control & Information; Sep2010, Vol. 27 Issue 3, p267
In this paper, the problem of exponential stability of the zero state equilibrium of a linear differential equation defined by an operator-valued function with positive evolution on an infinite-dimensional ordered Banach space is investigated. The class of linear differential equations...
- Linear quadratic regulator for time-varying hyperbolic distributed parameter systems.
AKSIKAS, ILYASSE; FORBES, J. FRASER // IMA Journal of Mathematical Control & Information; Sep2010, Vol. 27 Issue 3, p387
This paper addresses the linear quadratic (LQ) problem for a class of time-varying hyperbolic partial differential equation (PDEs) systems. The control method is based on two main ingredients: infinite-dimensional state space description and the well-known Riccati equation approach. First, the...
- Improving the Accuracy of the Solutions of Riccati Equations.
Vahidi, A. R.; Didgar, M. // International Journal of Industrial Mathematics; 2012, Vol. 4 Issue 1, p11
In this paper, we present an improved method for solving Riccati equations. This modification is based on the previous scheme to obtain the approximate solution of Riccati equations [B.Q. Tang and X.F. Li, A new method for determining the solution of Riccati differential equations, Appl. Math....
- Classical Solutions of Nonautonomous Riccati Equations Arising in Parabolic Boundary Control Problems, II.
Acquistapace, P.; Terreni, B. // Applied Mathematics & Optimization; 2000, Vol. 41 Issue 2, p199
Abstract. An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. We give the proof of some result stated in [AT5], and in...
- On the Stabilization of Nonlinear Continuous-Time Systems in Hilbert Spaces.
Phat, Vu N.; Linh, Nguyen M. // Southeast Asian Bulletin of Mathematics; 2003, Vol. 27 Issue 1, p135
This paper deals with stabilization problem of a class of infinite-dimensional nonlinear continuous-time systems. We present some useful relations between infinite-dimensional controllability and Riccati operator equations in Hilbert spaces and then apply to the complete stabilization problem....
- OSCILLATION FOR FORCED SECOND-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES.
Mugen Huang; Weizhen Feng // Electronic Journal of Differential Equations; 2006, Vol. 2006, Special section p1
By means of Riccati transformation techniques, we present oscillation criteria for forced second-order nonlinear dynamic equations on time scales. These results are based on the information on a sequence of subintervals of [a, 8) only, rather than on the whole half-line.
- A method of constructing Lyapunov functions of continuous TSK fuzzy model.
ZHIGANG YU; QI FEI // IMA Journal of Mathematical Control & Information; Sep2005, Vol. 22 Issue 3, p251
Stability of system with continuous TSK fuzzy model is analysed on the basis of Tanaka's theorem. An approach to construct Lyapunov's functions of a class of systems by solving Riccati inequalities or Riccati equations is presented.
- The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations.
Jianping Zhao; Bo Tang; Kumar, Sunil; Yanren Hou // Mathematical Problems in Engineering; 2012, Vol. 2012, Special section p1
An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansatz and Backlund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time...
- On Lie systems and Kummer-Schwarz equations.
de Lucas, J.; Sardón, C. // Journal of Mathematical Physics; Mar2013, Vol. 54 Issue 3, p033505
A Lie system is a system of first-order differential equations admitting a superposition rule, i.e., a map that expresses its general solution in terms of a generic family of particular solutions and certain constants. In this work, we use the geometric theory of Lie systems to prove that the...
- Generalized Variational Oscillation Principles for Second-Order Differential Equations with Mixed-Nonlinearities.
Jing Shao; Fanwei Meng; Xinqin Pang // Discrete Dynamics in Nature & Society; 2012, Special section p1
Using generalized variational principle and Riccati technique, new oscillation criteria are established for forced second-order differential equation with mixed nonlinearities, which improve and generalize some recent papers in the literature.
- A New Oscillation Criterion for Forced Second-Order Quasilinear Differential Equations.
Shao Jing // Discrete Dynamics in Nature & Society; 2011, Special section p1
By using the generalized variational principle and Riccati technique, a new oscillation criterion is established for second-order quasilinear differential equation with an oscillatory forcing term, which improves and generalizes some of new results in the literature.
- Special Solutions to the Second q-PainlevÃ© Equation.
Ohyama, Yousuke // AIP Conference Proceedings; 9/30/2010, Vol. 1281 Issue 1, p1714
The second q-PainlevÃ© equation has two formal solutions around the infinity. This series converges only for |q| = 1. If q is a root of unity, this series expresses an algebraic function.
- Numerical solution of multiband kÂ·p model for tunnelling in type-II heterostructures.
Botha, A. E. // South African Journal of Science; Jul/Aug2009, Vol. 105 Issue 7/8, p294
A new and very general method was developed for calculating the charge and spin-resolved electron tunnelling in type-II heterojunctions. Starting from a multiband kÂ·p description of the bulk energy-band structure, a multiband kÂ·p Riccati equation was derived. The reflection and...
- The Taylor Matrix Method for Approximate Solution of Lane-Emden Equation with index-n.
Guler, Coskun; Emiroglu, Ibrahim; Tasci, Fatih; Sivri, Mustafa // Applied Mathematics & Information Sciences; Jul2013, Vol. 7 Issue 4, p1341
Many problems in mathematical physics can be formulated as an equation of Lane-Emden type. There are many methods for the solution of this equation. One of these methods is the Taylor matrix method. The only types of nonlinear equations that this method has been applied so far are the Riccati...
- DEFLATING IRREDUCIBLE SINGULAR M-MATRIX ALGEBRAIC RICCATI EQUATIONS.
WEI-GUO WANG; WANG, WEI-CHAO; LI, REN-CANG // Numerical Algebra, Control & Optimization; Sep2013, Vol. 3 Issue 3, p491
A deflation technique is presented for an irreducible singular M- matrix Algebraic Riccati Equation (MARE). The technique improves the rate of convergence of a doubling algorithm, especially for an MARE in the critical case for which without deflation the doubling algorithm converges linearly...
- On the local and nonlocal Camassaâ€“Holm hierarchies.
Casati, Paolo; Lorenzoni, Paolo; Ortenzi, Giovanni; Pedroni, Marco // Journal of Mathematical Physics;
We construct the local and nonlocal conserved densities for the Camassaâ€“Holm equation by solving a suitable Riccati equation. We also define a Kadomtsevâ€“Petviashvili extension for the local Camassaâ€“Holm hierarchy.
- The Three-Step Master Equation: Class of Parametric Stationary Solutions.
Rosu, Haret C.; Reyes, Marco A.; Valencia, F. // International Journal of Theoretical Physics; Sep2005, Vol. 44 Issue 9, p1565
We examine the three-step master equation from the standpoint of the general solution of the associated discrete Riccati equation. We report by this means stationary master solutions depending on a free constant parameter, denoted by D, that should be negative in order to assure the positivity...
- Semiclassical coherent-state propagator for many particles.
Braun, Carol; Garg, Anupam // Journal of Mathematical Physics; Mar2007, Vol. 48 Issue 3, p032104
We obtain the semiclassical coherent-state propagator for a many-particle system with an arbitrary Hamiltonian.
- On Linearization by Generalized Sundman Transformations of a Class of LiÃ©nard Type Equations and Its Generalization.
Johnpillai, A. G.; Mahomed, F. M. // Applied Mathematics & Information Sciences; 2013, Vol. 7 Issue 6, p2355
We study the linearization of a class of LiÃ©nard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map...