Riccati equation

About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.

On the Control of a Linear Functional Differential Equation with Quadratic Cost

Abstract: Riccati-like linear functional differential equation with quadratic cost, analyzing feedback control solution existence and uniqueness

Control and estimation of distributed parameter systems

Abstract: The volume here presented contains the Proceedings of the International Conference on Control of Distributed Parameter Systems, held in Graz (Austria) from July 15–21, 2001. It was the one eighth in a series of conferences that began in 1982. The book includes are a broad variety of topics related to partial differential equations, ranging from abstract functional analytic framework to aspects of modelling, with the main emphasis, however, on theory and numerics of optimal control for nonlinear distributed parameter systems. The proceedings contain 16 articles written by 27 authors, each of the papers containing new research results, not published before. They give a very useful overview to many of the current theoretical and industrial problems. The upto-date references at the end of the articles are also very helpful, and the nice, uniform TeX style of the book will be appreciated by the readers. In what follows, I describe briefly the papers contained in this collection. 1 H.T. Banks, S.C. Beeler and H.T. Tran, State estimations and tracking control of nonlinear dynamical systems. Based on the ”state-dependent Riccati equation”, nonlinear estimators and nonlinear feedback tracking controls are constructed for a wide class of systems. An application to a flight dynamics simulation shows that the corresponding computational methods are easily implementable and efficient. H.T. Banks, H. Tran and S. Wynne, The well-posedness results for a shear wave propagation model. Existence and uniqueness results are established for a nonlinear model for propagation of shear waves in viscoelastic tissue. R. Becker and B. Wexler, Mesh adaptation for parameter identification problems. The authors consider automatic mesh refinement for parameter identification problems involving PDEs. The idea is to solve the inverse problem on a ”cheap” discrete model, which still captures the ”essential” features of the physical model. To this end, a posteriori error estimator is used to successively

A Riccati equation in radiative stellar collapse

Abstract: We model the behavior of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behavior is a Riccati equation. We show that the Riccati equation admits two classes of new solutions in closed form. We regain particular models, obtained in previous investigations, as special cases. A significant feature of our solutions is the general spatial dependence in the metric functions which allows for a wider study of the physical features of the model, such as the behavior of the causal temperature in inhomogeneous space-times.