A Riccati Equation for Stochastic

On the parameter dependence of a class of rational matrix equations occurring in stochastic optimal control

This paper is concerned with rational matrix equations occuring in stochastic control that play an analogous role as the algebraic Riccati equation does in deterministic control. We will therefore sometimes refer to these equations as stochastic (algebraic) Riccati equations. A first rigorous treatment of a stochastic Riccati equation from LQ-control theory seems to have been undertaken by Wonh...

Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati

A stochastic linear quadratic (LQ) control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite. Indefinite stochastic LQ theory has been extensively developed and has found interesting applications in finance. However, there remains an outstanding open problem, which is to identify an appropriate Riccati-type equation whose solvabili...

Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation

We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential Riccati equation, called the generali...

Iterative Solution of a Nonsymmetric Algebraic Riccati Equation

We study the nonsymmetric algebraic Riccati equation whose four coefficient matrices are the blocks of a nonsingular M -matrix or an irreducible singular M -matrix M . The solution of practical interest is the minimal nonnegative solution. We show that Newton’s method with zero initial guess can be used to find this solution without any further assumptions. We also present a qualitative perturb...

Application of Iterative Methods for Solving General Riccati Equation

An exponential spline for solving the fractional riccati differential equation

In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the me...