In this paper, we study the existence of solutions to a degenerate algebraic Riccati equation associated to an optimal control problem with infinite time horizon. Under some assumptions on the control system, we can select a solution to this Riccati equation providing a feedback control law able to stabilize the system.

This paper proposes a new representation for the predictor estimates recursion and corresponding Riccati equation for discrete-time, time-variant descriptor systems. The introduced “9-block” form for the predictor and Riccati equation presents an interesting simple and symmetric structure, which enable us to treat directly the most general systems where state and measurement noises are correlat...

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 the classic problem of minimizing a quadratic cost functional for well-posed linear systems over the class of inputs that are square integrable and that produce a square integrable output. As is well-known, the minimum cost can be expressed in terms of a bounded nonnegative selfadjoint operator X that in the finite-dimensional case satisfies a Riccati equation. Unfortunately, the in...

In this paper, the Exp-function method is used to seek generalized solitonary solutions of Riccati equation. Based on the generalized solitonary solutions of Riccati equation, some new exact solutions of the the classical Drinfel’d-Sokolov-Wilson equation are obtained by F-expansion method. It is shown that the F-expansion method combined with Expfunction method (F-Exp method) provides a straig...

A method for finding solutions of the Riccati differential equation y′ = P (x) + Q(x)y + R(x)y2 is introduced. Provided that certain relations exist between the coefficient P (x), Q(x) and R(x), the above equation can be solved in closed form. We determine the required relations and find the general solutions to the aforementioned equation. The method is then applied to the Riccati equation ari...

We generalize the classical theory on algebraic Riccati equations and optimization to infinite-dimensional well-posed linear systems, thus completing the work of George Weiss, Olof Staffans and others. We show that the optimal control is given by the stabilizing solution of an integral Riccati equation. If the input operator is not maximally unbounded, then this integral Riccati equation is equ...

This paper is concerned with a stochastic linear quadratic (LQ) control problem in the infinite time horizon, with indefinite state and control weighting matrices in the cost function. It is shown that the solvability of this problem is equivalent to the existence of a so-called static stabilizing solution to a generalized algebraic Riccati equation. Moreover, another algebraic Riccati equation...

Kudryashov in [ Phys. Lett. A 342 (2005) 99-106] used simplest nonlinear differential equations like the Riccati equation, the equation for the Jacobi elliptic function to present a new approach for searching exact solutions of nonlinear partial differential equations. As application, he obtained a kind of exact solutions to the Fisher equation. In this letter, more explicit exact solitary wave...

the extended homogeneous balance method is used to construct exacttraveling wave solutions of the maccari system, in which thehomogeneous balance method is applied to solve the riccati equationand the reduced nonlinear ordinary differential equation. many exacttraveling wave solutions of the maccari system equation aresuccessfully obtained.