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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.


Papers
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Journal ArticleDOI
TL;DR: In this article, the problem of direct numerical integration of differential Riccati equations (DREs) and some related issues are considered, and a useful matrix interpretation is given for many integration schemes, such as backward differentiation formulas, when applied to the DRE.
Abstract: . In this paper the problem of direct numerical integration of differential Riccati equations (DREs) and some related issues are considered. The DRE is an expression of a particular change of variables for a linear system of ordinary differential equations. The error that an approximate solution of the DRE induces on the original variables of the system is considered, and it is related to geometrical properties of the system itself. Sharp bounds on the global error for the computed solution are also given in terms of local errors and geometrical properties of the original system. Nonstiff and stiff DREs of unsymmetric and symmetric type are considered. A useful matrix interpretation is given for many integration schemes (such as the backward differentiation formulas, BDF), when applied to the DRE. This allows the matrix structure of the problem to be exploited. In particular, for stiff DREs, the resulting strategy allows for a saving of three orders of magnitude with respect to the standard reform...

104 citations

Journal ArticleDOI
En-Gui Fan1
TL;DR: In this paper, a direct and unified algorithm for constructing multiple travelling wave solutions of nonlinear partial differential equations (PDEs) is presented and implemented in a computer algebraic system.
Abstract: In this paper, a direct and unified algorithm for constructing multiple travelling wave solutions of nonlinear partial differential equations (PDEs) is presented and implemented in a computer algebraic system. The key idea of this method is to take full advantage of a Riccati equation involving a parameter and use its solutions to replace the tanh-function in the tanh method. It is quite interesting that the sign of the parameter can be used to exactly judge the number and types of such travelling wave solutions. In this way, we can successfully recover the previously known solitary wave solutions that had been found by the tanh method and other more sophisticated methods. More importantly, for some equations, with no extra effect we also find other new and more general solutions at the same time. By introducing appropriate transformations, our method is further extended to the nonlinear PDEs whose balancing numbers may be any nonzero real numbers. The efficiency of the method can be demonstrated on a large variety of nonlinear PDEs such as those considered in this paper, Burgers-Huxley equation, coupled Korteweg-de Vries equation, Caudrey-Dodd-Gibbon-Kawada equation, active-dissipative dispersive media equation, generalized Fisher equation, and nonlinear heat conduction equation.

104 citations

Journal ArticleDOI
TL;DR: A unified model to describe the mixed uncertainties of random delays, packet dropouts and uncertain observations by three Bernoulli distributed random variables with known distributions is developed via an innovation analysis approach.
Abstract: This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random sensor delays, packet dropouts and uncertain observations. We develop a unified model to describe the mixed uncertainties of random delays, packet dropouts and uncertain observations by three Bernoulli distributed random variables with known distributions. Based on the proposed model, the optimal linear estimators that only depend on probabilities are developed via an innovation analysis approach. Their solutions are given in terms of a Riccati equation and a Lyapunov equation. They can deal with the optimal linear filtering, prediction and smoothing for systems with random sensor delays, packet dropouts and uncertain observations in a unified framework. Simulation results show the effectiveness of the proposed optimal linear estimators.

104 citations

Journal ArticleDOI
TL;DR: In this article, the stochastic linear quadratic optimal control problem (LQ problem) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable is studied.
Abstract: This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward—backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.

104 citations

Dissertation
01 Jan 1970
TL;DR: The Riccati equation is studied from an algebraic point of view, and the results are applied on optimal control of linear time invariant systems with quadratic loss.
Abstract: The matrix Riccati equation appears in many optimal control and filtering problems. In this paper the Riccati equation is studied from an algebraic point of view, and the results are applied on optimal control of linear time invariant systems with quadratic loss.

104 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023153
2022335
2021203
2020240
2019223
2018231