Topic
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.
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TL;DR: On the basis of analysis to the projective Riccati equations, an intermediate transformation in expansion method is constructed, and this transformation is applied to solve Gardner equation, there many new kinds of travelling wave solutions including solitary wave solution are obtained, in which some are found for the first time as discussed by the authors.
Abstract: On the basis of analysis to the projective Riccati equations, an intermediate transformation in expansion method is constructed. And this transformation is applied to solve Gardner equation, there many new kinds of travelling wave solutions including solitary wave solution are obtained, in which some are found for the first time.
79 citations
TL;DR: In this paper, the energy method was used to obtain a desired decay estimate for the linearized Boltzmann equation with respect to the existence of global solutions near a Maxwellian.
Abstract: The initial value problem for the nonlinear Boltzmann equation is studied. For the existence of global solutions near a Maxwellian, it is important to obtain a desired decay estimate for the linearized equation. In previous works, such a decay estimate was obtained by a method based on the spectral theory for the linearized Boltzmann operator. The aim of this paper is to show the same decay estimate by a new method. Our method is the so-called energy method and makes use of a Ljapunov function for the ordinary differential equation obtained by taking the Fourier transform. Our Ljapunov function is constructed explicitly by using some property of the equations for thirteen moments.
79 citations
TL;DR: A new approach to quadratic stabilization of uncertain fuzzyynamic systems is developed and it is shown that the uncertain fuzzy dynamic system can be stabilized if a suitable RicCati equation or a set of Riccati equations has solutions.
Abstract: A new approach to quadratic stabilization of uncertain fuzzy dynamic systems is developed in this paper. This uncertain fuzzy dynamic model is used to represent a class of uncertain continuous time complex nonlinear systems which include both linguistic information and system uncertainties. It is shown that the uncertain fuzzy dynamic system can be stabilized if a suitable Riccati equation or a set of Riccati equations has solutions. Constructive algorithms are also developed to obtain the stabilization feedback control laws. Finally, an example is given to illustrate the application of the proposed method.
79 citations
TL;DR: In this paper, the finite-time regulator problem for linear, autonomous, degenerate systems is studied and two investigations of the regulator problem are presented, which depend on the quadratic cost associated with the differential equation.
Abstract: In this paper, we study the finite-time regulator problem for linear, autonomous, degenerate systems, i.e., systems described by the differential equation
$$K\dot x = Ax + Bu(t)$$
with det(K)=0. Two investigations of the regulator problem are presented, which depend on the quadratic cost associated with the differential equation.
79 citations
TL;DR: In this article, an infinite-dimensional linear time-varying system on the interval $( - ∞, ∞ )$ is considered and three quadratic problems: the infinite horizon problem, and one-sided and two-sided average cost problems.
Abstract: An infinite-dimensional linear time-varying system on the interval $( - \infty ,\infty )$ is considered. We introduce three quadratic problems: the infinite horizon problem, and one-sided and two-sided average cost problems. A Riccati equation on $( - \infty ,\infty )$ is considered first and sufficient conditions for the existence and uniqueness of a bounded solution are given. Then by dynamic programming the quadratic problems are solved. Similar problems in the stochastic case are considered.
78 citations