In this paper, we study Riccati solutions of Painlevé equations from a view point of geometry of Okamoto-Painlevé pairs (S,Y ). After establishing the correspondence between (rational) nodal curves on S − Y and Riccati solutions, we give the complete classification of the configurations of nodal curves on S − Y for each Okamoto–Painlevé pair (S, Y ). As an application of the classification, we ...

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.

In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathemati...

The numerical treatment of the linear-quadratic optimal control problem requires the solution of Riccati equations. In particular, the differential Riccati equations (DRE) is a key operation for the computation of the optimal control in the finite-time horizon case. In this work, we focus on large-scale problems governed by partial differential equations (PDEs) where, in order to apply a feedba...

In this paper, we present a numerical method for solving large continuous-time algebraic Riccati equations. This method is based on the global FOM algorithm and we call it by global FOM-Riccati-Like (GFRL) algorithm .

A Riccati-equation based state-space solution to the H 1-optimal control problem for periodic multirate sampled-data systems is presented. The solution is characterized by two standard discrete algebraic Ric-cati equations with a set of associated matrix positive deeniteness conditions and coupling criteria. The equations are derived by discretizing a pair of coupled periodic Riccati diierentia...

We consider a set of continuous algebraic Riccati equations with indefinite quadratic parts that arise in H∞ control problems. It is well known that the approach for solving such type of equations is proposed in the literature. Two matrix sequences are constructed. Three effective methods are described for computing the matrices of the second sequence, where each matrix is the stabilizing solut...

State-space formulas are derived for the minimum-entropy H∞ controller when the plant and controller are constrained to be block-lower-triangular. Such a controller exists if and only if: the corresponding unstructured problem has a solution, a certain pair of coupled algebraic Riccati equations admits a mutually stabilizing fixed point, and a pair of spectral radius conditions is met. The cont...

In this paper, a spectral Tau method for solving fractional Riccati differential equations is considered. This technique describes converting of a given fractional Riccati differential equation to a system of nonlinear algebraic equations by using some simple matrices. We use fractional derivatives in the Caputo form. Convergence analysis of the proposed method is given and rate of convergence ...