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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01 Jan 2004
TL;DR: In this article, the authors consider the numerical solution of differential Riccati equations and investigate whether they are suitable for large-scale problems arising in LQR and LQG design for semi-discretized partial differential equations.
Abstract: We consider the numerical solution of differential Riccati equations. We review the existing methods and investigate whether they are suitable for large-scale problems arising in LQR and LQG design for semi-discretized partial differential equations. Based on this review, we suggest an efficient matrix-valued implementation of the BDF for differential Riccati equations.
54 citations
TL;DR: The G^'G method is applied to carry out the integration of this equation and using the ansatz method this equation is integrated in (1+2) dimensions with power law nonlinearity.
54 citations
TL;DR: In this article, generalized Riccati differential and difference equations obtained from standard RICCati equations by adding a semidefinite perturbation term were investigated and results on the monotonic dependence of the solutions on the coefficients and initial values as well as results on convergence of solutions were given.
54 citations
TL;DR: In this paper, the Riccati equation was used to construct the soliton solutions for pulse propagation equation with z-dependent coefficients, and the periodic wave and the optical soliton solution were obtained for the pulse propagation equations with dependent coefficients.
54 citations
TL;DR: A novel solution to the full order anti-windup (AW) compensation problem for stable systems with input saturation is given by “completing the square” in three steps and requires the solution to a single bounded-real Riccati equation, characterized by the open-loop plant's norm.
Abstract: The aim of this paper is to give a novel solution to the full order anti-windup (AW) compensation problem for stable systems with input saturation. The solution is obtained by “completing the square” in three steps and requires the solution to a single bounded-real Riccati equation, characterized by the open-loop plant's norm. The Riccati equation plays the role of the LMIs usually found in anti-windup synthesis, but, in addition to its numerical advantages, it yields a family of anti-windup compensators with the same performance. This family of compensators is parameterized by a matrix which is intimately linked with both the poles of the anti-windup compensator and the robustness properties of the closed-loop saturated system. Thus, this matrix allows a robust anti-windup problem to be solved in a straightforward and intuitive manner. The effectiveness of the proposed technique is demonstrated on a simple example.
54 citations