Estimation of Maximal Existence Intervals for Solutions to a Riccati Equation via an Upper-Lower Solution Method
نویسندگان
چکیده
Denote by ’ the set of all real symmetric matrices. We use to 8 ‚ 8 K L K L a b denote that is positive semidefinite (definite). For or K L M œ > ß > c d ! 0 Ð_ß > Ó 0 and \ œ P Mß 8 ‚ 8 V \ 8‚8 or ’ _ , denote by the space of all bounded and measurable a b functions from to and by the space of all with M \ P Mß T − P Mß "ß_ _ a b a b \ \ T − P Mß P Mß − P Mß w _ _ _ 8 a b a b a b \ E − V Fß U T − . , and Suppose . Consider the 8‚8 8 0 ’ ’ classical differential Riccati equation Xa b T ́ T E T T E U T FT œ !ß T > œ T w 0 0 X a b , (1)
منابع مشابه
Upper-Lower Solution Method for Differential Riccati Equations from Stochastic LQR Problems
We use upper and lower solutions to study the existence and properties of solutions to differential Riccati equations arising from stochastic linear quadratic regulator (LQR) problems. The main results include an interpretation of upper and lower solutions, comparison theorems, an upper-lower solution theorem, necessary and sufficient conditions for existence of solutions, an estimation of maxi...
متن کاملIterative scheme to a coupled system of highly nonlinear fractional order differential equations
In this article, we investigate sufficient conditions for existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of th...
متن کاملApplication of fractional-order Bernoulli functions for solving fractional Riccati differential equation
In this paper, a new numerical method for solving the fractional Riccati differential equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon fractional-order Bernoulli functions approximations. First, the fractional-order Bernoulli functions and their properties are presented. Then, an operational matrix of fractional order integration...
متن کاملA Solution of Riccati Nonlinear Differential Equation using Enhanced Homotopy Perturbation Method (EHPM)
Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...
متن کاملSolutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...
متن کامل