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On a degenerate Riccati equation ∗ by
"... Abstract: 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 la ..."
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Abstract: 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
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
 Proc. Japan Acad. Ser. A 65
, 1989
"... This paper treats degenerate parabolic equations of second order (1.1) u t + F{Vu, V 2 w) = 0 ..."
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Cited by 370 (16 self)
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This paper treats degenerate parabolic equations of second order (1.1) u t + F{Vu, V 2 w) = 0
Optimal control and Riccati equation
"... In this paper, we consider a stabilization problem for a fluid flow. For a perturbation of the velocity of an incoming flow on a flat plate, the laminartoturbulent transition location varies. We want to stabilize it by a suction velocity trough the plate. The linearization of the nonlinear model a ..."
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around a steady state solution leads to a linear degenerate parabolic equation. We look for a suction velocity in a feedback form, determined by solving a LQR problem with an infinite time horizon. We derive the associated optimality system and the optimal control. The study of the Riccati equation
A Schur method for solving algebraic Riccati equations
 IEEE Trans. Auto. Control
, 1979
"... Abstract. An exact line search method has been introduced by Benner and Byers [IEEE Trans. Autom. Control, 43 (1998), pp. 101–107] for solving continuous algebraic Riccati equations. The method is a modification of Newton’s method. A convergence theory is established in that paper for the Newtonlik ..."
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Cited by 174 (3 self)
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Abstract. An exact line search method has been introduced by Benner and Byers [IEEE Trans. Autom. Control, 43 (1998), pp. 101–107] for solving continuous algebraic Riccati equations. The method is a modification of Newton’s method. A convergence theory is established in that paper for the Newton
Solving ForwardBackward Stochastic Differential Equations Explicitly – a Four Step Scheme
 Prob. Th. Rel. Fields
, 1994
"... Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability ..."
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Cited by 243 (19 self)
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in control theory, using some functional analysis, we obtain a necessary and su cient condition for the solvability of the linear FBSDEs with the processes Z (serves as a correction, see x1) being absent in the drift. Then a Riccati type equation for matrixvalued (not necessarily square) functions
A PDEBased Fast Local Level Set Method
 Journal of Computational Physics
, 1999
"... this paper we localize the level set method. Our localization works in as much generality as does the original method and all of its recent variants [27, 28], but requires an order of magnitude less computing effort. Earlier work on localization was done by Adalsteinsson and Sethian [1]. Our approac ..."
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Cited by 266 (26 self)
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approach differs from theirs in that we use only the values of the level set function (or functions, for multiphase flow) and not the explicit location of points in the domain. Our implementation is easy and straightforward and has been used in [9, 14, 27, 28]. Our approach is partial differential equation
Riccati equation
, 2000
"... On a SUSY QM scheme for any linear homogeneous differential equation of the second order ..."
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On a SUSY QM scheme for any linear homogeneous differential equation of the second order
APPROXIMATION OF SOLUTIONS OF RICCATI EQUATIONS
, 2005
"... This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite dimensional approximants. ..."
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Cited by 3 (0 self)
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This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite dimensional approximants
on The Riccati Equation in Mathematical Finance
"... This paper uses ideas from symbolic computation to classify solutions to an important class of problems in mathematical finance and thus provides a linkage between these two fields. We show that Kovacic’s concept of closedform solutions to the Riccati ordinary differential equation can be used to p ..."
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Cited by 5 (0 self)
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This paper uses ideas from symbolic computation to classify solutions to an important class of problems in mathematical finance and thus provides a linkage between these two fields. We show that Kovacic’s concept of closedform solutions to the Riccati ordinary differential equation can be used
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