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: In this article, a parametrization of the solution set of the algebraic Riccati equation and its inequality of optimal control is presented, where only sign-controllability of the underlying system is assumed.
58 citations
58 citations
10 Dec 2002
TL;DR: In this article, a nonlinear control synthesis technique (/spl theta/ - D approximation) is presented, which achieves suboptimal solutions to nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman (HJB) equation approximately by adding perturbations to the cost function.
Abstract: In this paper, a new nonlinear control synthesis technique (/spl theta/ - D approximation) is presented. This approach achieves suboptimal solutions to nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman (HJB) equation approximately by adding perturbations to the cost function. By manipulating the perturbation terms both semi-globally asymptotic stability and suboptimality properties can be obtained. The convergence and stability proofs are given. This method overcomes the large control for large initial states problem that occurs in some other Taylor expansion based methods. It does not need time-consuming online computations like the state dependent Riccati equation (SDRE) technique. A vector problem is investigated to demonstrate the effectiveness of this new technique.
58 citations
TL;DR: A spline approximation method for computation of the gain operators in feedback controls is proposed and tested numerically and compares with a method based on “averaging” approximations.
Abstract: We consider the infinite interval regulator problem for systems with delays. A spline approximation method for computation of the gain operators in feedback controls is proposed and tested numerically. Comparison with a method based on “averaging” approximations is made.
58 citations
TL;DR: In this article, a Riccati differential equation for the reflection of electromagnetic waves from a plane interface separating a vacuum half-space and a stratified anisotropic layer is presented.
Abstract: A direct approach to the investigation of the reflection of electromagnetic waves from a plane interface separating a vacuum half-space and a stratified anisotropic layer is presented. The formulation involves the generation of a Riccati differential equation for a certain 2*2 reflection matrix. The approach is already well established for scalar problems, but its implementation in cases which allow mode conversion is believed to be new. The reflection matrix concerned is unitary when the anisotropic layer is nondissipative, and an efficient numerical method to solve the equation is outlined. Sample results are presented to illustrate the theory. >
58 citations