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: It is shown that the solution to every matrix Riccati equation can be generated by the resolvent of a certain Fredholm integral operator and, conversely, this Resolvent can be determined from the corresponding Riccatis solution.
66 citations
TL;DR: In this paper, a simple method of finding exact solutions of nonlinear partial differential equations (PDEs) is introduced, which is based on comparing nonlinear differential equations obtained from PDEs with standard differential equations having solution in the form of the logistic function.
66 citations
TL;DR: In this paper, an asymptotic expansion method was developed for a singularly perturbed matrix Riccati equation, which can be used in the design of regulator and estimator systems with small parameters.
Abstract: An asymptotic expansion method is developed for a singularly perturbed matrix Riccati equation. The method reduces the system order and avoids difficulties with numerically stiff problems. It can be used in the design of regulator and estimator systems with small parameters.
66 citations
TL;DR: In this paper, it is shown that the data-to-solution map for the Degasperis-Procesi (DP) equation is not a uniformly continuous map on bounded subsets of Sobolev spaces with exponent greater than 3/2.
Abstract: It is shown in both the periodic and the non-periodic cases that
the data-to-solution map for the Degasperis-Procesi (DP) equation
is not a uniformly continuous map on
bounded subsets of Sobolev spaces with exponent greater than 3/2.
This shows that continuous dependence on initial data of solutions to
the DP equation is sharp.
The proof is based on well-posedness results and approximate solutions.
It also exploits the fact that DP solutions conserve
a quantity which is equivalent to the $L^2$ norm.
Finally, it provides an outline of the local well-posedness proof
including the key estimates for the size of the solution and for the solution's lifespan that are
needed in the proof of the main result.
66 citations
TL;DR: In this article, an iterative algorithm to solve algebraic Riccati equations with an indefinite quadratic term is proposed, and the global convergence and local quad ratic rate of convergence are guaranteed and a proof is given.
Abstract: An iterative algorithm to solve algebraic riccati equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.
66 citations