We study backward stochastic Riccati equations (BSREs) arising in quadratic optimal control problems with infinite dimensional stochastic differential state equations. We allow the coefficients, both in the state equation and in the cost, to be random. In such a context BSREs are backward stochastic differential equations living in a non-Hilbert space and involving quadratic non-linearities. We...

An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of such equations (including the existence of solutions) driven by one-dimensional Brownian motion. The idea is to replace the original equation by a system of BS...

based on symbolic manipulation program maple and using riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient broer--kaup system in quite a straightforward manner. the known solutions of riccati equation are used to construct new solutions for variable coefficient broe...

This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite dimensional approximants. The theory of exponentially dichotomous operators and bisemigroups is instrumental in our approach.

A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field forward-backward stochastic differential equation. Using a decoupling technique, two Riccati differential equations are obtained, which are uniquely solvable...

The generalized Riccati equation mapping is extended with the basic G′/G -expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the 2 1 -dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation G′ η w uG η...

in this paper mathematical extensions and generalizations of the pearl-reed model for'growth with saturation are discussed. the derived differential equation are of bernoulli and riccati type that owing to their special forms could be explicitely integrated resulting in closed form solutions. the asymptotic bahaviour of the system in each case is briefly examined and the results are compar...

We present a simple SUSY n=2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get selfconsistent systems of coupled differential equations for the components of the superfield. This procedure is applie...

A solution X of a discrete-time algebraic Riccati equation is called unmixed if the corresponding closed-loop matrix Φ(X) has the property that the common roots of det (sI−Φ(X)) and det (I− sΦ(X)∗) (if any) are on the unit circle. A necessary and sufficient condition is given for existence and uniqueness of an unmixed solution such that the eigenvalues of Φ(X) lie in a prescribed subset of C. A...

This paper develops an anti-windup scheme for systems with rate-limited actuators. The main results show how a full-order anti-windup compensator can be synthesised using an algebraic Riccati equation and several free parameters. A further result then shows how the free parameters may be chosen to influence, in an intuitive way, the local L2 gain of the system and the size of the region of attr...