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Topic: Riccati

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	Riccati equation - Wikipedia, the free encyclopedia
		It is named after Count Jacopo Francesco Riccati (1676-1754).
		As explained on pages 23-25 of Ince's book, the non-linear Riccati equation can always be reduced to a second order linear ordinary differential equation (ODE).
		Riccati Equation at EqWorld: The World of Mathematical Equations.
	en.wikipedia.org /wiki/Riccati_equation (471 words)

	Mailgate: sci.stat.math: Anatomy and Physiology of the Riccati Equation (Site not responding. Last check: 2007-10-30)
		The difference in signs of the y and y^2 terms plays a similar role to its role in the special Riccati Equation that is the Logis- tic differential equation, in which expansive versus supply-limited contractive influences trade off via the y versus y^2 terms with their different signs.
		The number of roots of an algebraic equation decreases in essence at least as its degree decreases, and in terms of statistical (and non-statistical) modelling this means that non-oscillating behavior increases proportionately as the degree approaches 1 or 2.
		The Riccati differential equation is of degree 2 in y, despite its form dy/dt = A(t) + B(t)y + C(t)y^2.
	mailgate.supereva.it /sci/sci.stat.math/msg10415.html (493 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		c c as usual, the purpose of the riccati equation is that one of c decoupling the above matrix A(t).
		c stiffness occurs when the frechet derivative (jacobian) of the riccati c equation has one of its eigenvalues with real part negative and c large in magnitude, compared to the reciprocal of the t span of interest.
		c c (author of the solver for riccati equations) c luca dieci () c school of mathematics c georgia institute of technology c atlanta, ga 30332 c c () author to whom correspondance related to the riccati c equation should be addressed, and unique responsible c for the possible mulfunctioning of this c riccati solver.
	www.netlib.org /ode/dresol.f (15033 words)

	The Galileo Project
		His father died in 1686, when Riccati was only ten, but in view of Riccati's own life, they must have been wealthy.
		Riccati pursued questions over the whole range of science in his day.
		I Riccati e la cultura della marca nel settecento europeo, Atti del convegno internazionale di studio, Castelfranco Veneto, 5-6 Aprile, 1990, (Biblioteca di Nuncius, Studi e testi, 5), (Firenze, 1992).
	galileo.rice.edu /Catalog/NewFiles/riccati.html (540 words)

	The Solution of the Riccati Equation (Site not responding. Last check: 2007-10-30)
		Because the Riccati equation does not lend itself to solution by the techniques that produce solutions to linear differential equations typically the analysis is stalled.
		Moreover because of the similarity of the Riccati equation to the equations analyzed in Chaos Theory there is a presumption that further analysis will involve the concepts of Chaos Theory.
		The first important result in the analysis of the Riccati equation is that if one solution is known then a whole family of solutions can be found.
	www.applet-magic.com /riccati.htm (258 words)

	Andrea Luchesi, and his role in the birth of Haydn, Mozart and Beethoven myths
		Giordano Riccati, with his "Saggio sulle leggi del contrappunto" (1762) ("Essay on the counterpoint laws") published Vallotti's system aiming to "demonstrate, against the opinion of the modern mathematicians, that music is not just a sentimental art or an art of pure practice, but that it is a real mathematical science".
		Riccati attended to Vallotti's theory application through the teaching activity and the careful correction of the works done by several musicians addressing to him for suggestions and judgements.
		Giordano Riccati's conceiving of architecture can easily compared to that of music: mathematics and, more in general, the rational approach, cannot be left out from the human, culturale engagement, in every discipline, in every phase of the creating process of a work.
	itis.volta.alessandria.it /episteme/ep4/ep4tabog.htm (4891 words)

	Springer Online Reference Works
		Riccati (1723, see [1]); individual cases of the equation were examined earlier.
		are continuous functions, is called a general Riccati equation (as distinct from (1), which is called a special Riccati equation).
		Other cases of the integrability of general Riccati equations have also been studied (see [2]).
	eom.springer.de /r/r081770.htm (531 words)

	Vincent Riccati, S.J.
		Vincent Riccati, S.J. was born in Castel-Franco, Italy.
		His father Jacobi (after whom is named the Riccati differential equation) was one of the principal Italian mathematicians of the century, and his brother Giovanni was also a prominent mathematician.
		Riccati's development of the hyperbolic functions may be described as follows.
	www.faculty.fairfield.edu /jmac/sj/scientists/riccati.htm (1000 words)

	Riccati Equations
		In a number of mathematical and physical situations, a general Riccati differential equation arises and needs to be solved.
		It is easy, however, to construct Riccati equations that have trivial initial solutions, yet are not solvable by ordinary techniques such as separation of variables.
		This is the desired Riccati equation in z.
	zoo.cs.yale.edu /classes/cs490/99-00b/hillar.christopher.cjh26 (1945 words)

	Riccati Equations
		Before we give the formal definition of Riccati equations, a little introduction may be helpful.
		Riccati looked at the approximation to the second degree: he considered equations of the type
		We also recognize that the equation is of Riccati type.
	www.sosmath.com /diffeq/first/riccati/riccati.html (299 words)

	Jacopo Riccati - Wikipedia, the free encyclopedia
		Jacopo Francesco Riccati (28 May 1676 - 15 April 1754) was an Italian mathematician, born in Venice.
		He is now remembered for the Riccati equation.
		This article about a mathematician is a stub.
	en.wikipedia.org /wiki/Jacopo_Riccati (65 words)

	The Riccati Transformation
		Equation (15) is known as the Riccati equation associated with the system (2).
		The Riccati equation associated with the system (8) associated with the Airy equation is
		A picture representing the slope field, and several trajectories, of equation (16) is shown in Figure 8.
	www.cecm.sfu.ca /organics/papers/hubbard/paper/html/node8.html (221 words)

	Non-symmetric Matrix Riccati Equations (Site not responding. Last check: 2007-10-30)
		We prove a fundamental representation formula for all solutions of the matrix Riccati differential equation (RDE) and of the corresponding algebraic Riccati equation (ARE).
		R.S. Bucy, Structural stability for the Riccati equation, SIAM J.
		Medanic, Geometric properties and invariant manifolds of the Riccati equation, IEEE Trans.
	www.uni-duisburg.de /FB11/FGS/F7/Publications/ab42/ab42.html (571 words)

	riccati.html
		Depending on the case, the system may be able to solve the problem using one of the transformations above; they can also be used as departure point for guessing another transformation suitable for the given problem.
		Now, for c<>0, Riccati Special ODEs can be reduced, step by step, to the case c=0 provided that c can be written as c[n]=-4n/(2n-1) (integer n).
		The ideia is to change variables such as to obtain another ODE of type Riccati Special, but with c[n->0], until reaching c[0]=0.
	www.scg.uwaterloo.ca /~ecterrab/help/riccati1.html (461 words)

	Existence and Comparison Theorems for Algebraic Riccati Equations and Riccati Differential and Difference Equations (Site not responding. Last check: 2007-10-30)
		Moreover we obtain existence and comparison results for the maximal solutions of the corresponding generalized algebraic Riccati equations.
		For the symplectic matrix Riccati differential equation we derive sufficient conditions ensuring the global existence of the solutions of the corresponding initial value problems.
		KEY WORDS: Continuous-time Riccati equations, discrete-time Riccati equations, generalized Riccati equations, algebraic Riccati equations, Riccati inequalities, comparison theorems, global existence of solutions.
	www.uni-duisburg.de /FB11/FGS/F7/Publications/ab53/ab53.html (386 words)

	livre matrix riccati equations in control systems theory, (systems control : foundations applications), maths ... (Site not responding. Last check: 2007-10-30)
		The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control.
		Extensions to Riccati theory allow to tackle robust control problems in a unified approach.
		Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.
	www.lavoisier.fr /notice/fr402825.html (215 words)

	Riccati Difference Equation
		The Riccati difference equation is of the form
		of the Riccati difference equation is the set of initial conditions which the denominator c+dx
		Assume that the previous conditions hold and that the Riccati difference equation does possess a periodic solution of prime period two.
	hypatia.math.uri.edu /~kulenm/diffeqaturi/chad442/project.htm (336 words)

	Solutions of Generalized Riccati Differential Equations and their Approximation -Abstract (Site not responding. Last check: 2007-10-30)
		We study the solution of generalized matrix Riccati differential equations as they appear in differential games theory with various information structures.
		We propose a numerical approximation for the generalized Riccati differential equation arising from an optimally controlled differential game with memoryless feedback.
		Furthermore, we present an example of a generalized algebraic Riccati equation having several stabilizing positive semidefinite solutions.
	www.mathc.rwth-aachen.de /kun/abst5.html (126 words)

	Syllogismos - Riccati Vincenzo
		Riccati, V. De usu motus tractori in constructione Aequationum Differentialium Commentarius, Lelio della Volpe, Bologna
		In this work we can find a method based upon a physical model, suggested (but not proved) by Clairaut (1713-1765) in 1742: so Vincenzo Riccati did not try to obtain general methods to solve differential equations: he considered a particular class of problems and examinated such equations from an unusual point of wiew.
		If we move a thread from G to E, we trace a “tractoria” curve, so that when the extreme point of the thread is in E, the “punctum describens F” is in VZ, a curve with “initium abscissarum” in E. Finally we can trace KN parallel to FE: then GE =
	www.syllogismos.it /libristorici/riccativincenzo.htm (467 words)

	RR-4451 : A Direct Study in a Hilbert-Schmidt Framework of the Riccati Equation Appearing in a Factorization Method of ...
		In this paper, it was shown that, in the case of a cylinder, the boundary value problem can be factorized in two uncoupled first order initial value problems.
		This factorization utilizes the Dirichlet to Neumann operator which satisfies a Riccati equation.
		Cette factorisation fait intervenir l'opérateur Dirichlet-Neumann qui vérifie une équation de Riccati.
	www.inria.fr /rrrt/rr-4451.html (334 words)

	LQ control without Riccati equations
		A central issue is the stability of the feedback control; and we show this can be effectively examined through the complementary duality of the SDP.
		Furthermore, we establish several implication relations among the SDP complementary duality, the (generalized) Riccati equation, and the optimality of the LQ control problem.
		Based on these relations, we propose a numerical procedure that provides a thorough treatment of the LQ control problem via SDP: it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution.
	ideas.repec.org /p/dgr/eureir/1999150.html (298 words)

	AMCA: Matrix Riccati Differential Equations by K. Rajendra Prasad (Site not responding. Last check: 2007-10-30)
		The matrix Riccati differential equation is an interesting area of current research and it appears in a number of areas like biomathematics, control engineering and multi-dimensional transport processes.
		In this paper, we obtain the solution of the matrix Riccati differential equation and upper and lower bounds for the solution of the general matrix Riccati differential equation.
		Using quasi-linearization techniques, we convert the Riccati equations to Liapunov type matrix differential equations, and finally, we obtain the solutions of the Riccati equations.
	at.yorku.ca /c/a/c/r/46.htm (159 words)

	LQ control without Riccati equations
		We study a deterministic linear-quadratic (LQ) control problem over an infinite horizon, and develop a general apprach to the problem based on semi-definite programming (SDP)and related duality analysis.
		This approach allows the control cost matrix R to be non-negative (semi-definite), a case that is beyond the scope of the classical approach based on Riccati equations.
		We show that the complementary duality condition of the SDP is necessary and sufficient for the existence of an optimal LQ control.
	ideas.repec.org /p/dgr/eureir/1999140.html (297 words)

	Riccati Method
		I want to read a bit more example on using the Riccati Method when solvng D.E, who can help me?
		If can't~ no use of the Riccati method~
		For one, they give the solution right on the page, so I don't know why you think you can't do it (unless you mean that you're trying to solve it yourself and haven't looked at the answer).
	www.physicsforums.com /showthread.php?t=86288 (718 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Energy Citations Database (ECD) Document #4713560 - NOTE ON THE RICCATI EQUATION
		Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
		A simple modification of a method is proposed, which under certain circumstances produces both upper and lower bounds for the solution of the Riccati equation.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=4713560 (111 words)

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