We used what we called extended Fan’s sub-equation method and a new compound Riccati equations rational expansion method to construct the exact travelling wave solutions of the Davey-Stewartson DS equations. The basic idea of the proposed extended Fan’s subequation method is to take fulls advantage of the general elliptic equations, involving five parameters, which have many new solutions and w...

We consider the numerical solution of projected algebraic Riccati equations using Newton’s method. Such equations arise, for instance, in model reduction of descriptor systems based on positive real and bounded real balanced truncation. We also discuss the computation of low-rank Cholesky factors of the solutions of projected Riccati equations. Numerical examples are given that demonstrate the ...

Abstract: In this paper, we derive the analytical closed form solution of a class of Riccati equations. Since it is well known that to every Riccati equation there corresponds a linear homogeneous ordinary differential equation (ODE), the result obtained is subsequently employed to derive the analytical solution of the class of second order linear homogeneous ODEs corresponding to the class of ...

We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary s...

We consider multi-grid, or more appropriately, multi-level techniques for the numerical solution of operator Lyapunov and algebraic Riccati equations. The Riccati equation, which is quadratic, plays an essential role in the solution of linear-quadratic optimal control problems. The linear Lyapunov equation is important in the stability theory for linear systems and its solution is the primary s...

A multilayer recurrent neural network is proposed for solving continuous-time algebraic matrix Riccati equations in real time. The proposed recurrent neural network consists of four bidirectionally connected layers. Each layer consists of an array of neurons. The proposed recurrent neural network is shown to be capable of solving algebraic Riccati equations and synthesizing linear-quadratic con...

This paper presents a survey of some new applications of algebraic Riccati equations. In particular, the paper surveys some recent results on the use of algebraic Riccati equations in testing whether a system is negative imaginary and in synthesizing state feedback controllers which make the closed loop system negative imaginary. The paper also surveys the use of Riccati equation methods in the...

A generalized Chebyshev wavelet operational matrix (CWOM) is presented for the solution of nonlinear Riccati differential equations. The operational matrix together with suitable collocation points converts the fractional order Riccati differential equations into a system of algebraic equations. Accuracy and efficiency of the proposed method is verified through numerical examples and comparison...

In this paper, we study the existence of linear quadratic Gaussian (LQG)–balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show that the control (filter) Riccati equation has a nonnegative self-adjoint solution if and only if...

Minimum cost variance control (MCV) optimizes the variance of the cost function while the cost mean is kept at a prespecified level. The solutions of the infinite time horizon full-state-feedback MCV problem are found using the Hamilton-Jacobi theory. In the solutions of infinite time horizon MCV control problem, a pair of coupled algebraic Riccati equations arises. This paper considers the exi...