In this note, we show that under certain assumptions the scalar Riccati differential equation x′ = a(t)x + b(t)x + c(t) with periodic coefficients admits at least one periodic solution. Also, we give two illustrative examples in order to indicate the validity of the assumptions.

In this article, we use the Riccati transformation technique and some inequalities, to establish oscillation theorems for all solutions to evenorder quasilinear neutral differential equation “ˆ` x(t) + p(t)x(τ(t)) ́(n−1) ̃γ”′ + q(t)x ` σ(t) ́ = 0, t ≥ t0. Our main results are illustrated with examples.

The existence of a stabilizing solution to the non-symmetric algebraic Riccati equation is shown to be equivalent to the invertibility of a certain Toeplitz operator, whose symbol is the transfer matrix function of an exponentially dichotomic system. We also show that this theory has an important application to non-cooperative differential games.

We will consider He’s variational iteration method for solving fractional Riccati differential equation. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converges to the exact solution of the problem. The present method performs extremely well in terms of efficiency ...

A nonlinear feedback control strategy is presented where the feedback control is augmented with feedback gain sensitivity partial derivatives for handling model uncertainties. Derivative enhanced optimal feedback control is shown to be robust to large changes in the model parameters. The OCEA (Object Oriented Coordinate Embedding) computational differentiation toolbox is used for automatically ...

We study the variations of the quadratic performance associated to a linear differential system of retarded type for small values of the delays. From an interpretation of delays as singular perturbations of abstract evolution operators, we revisit the usual theory of representation and optimal control of retarded systems. This leads to a new parameterization of associated Riccati operators for ...

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...

A differential equation of a Riccati type for the diffuse reflection coefficient of a stratified sea is proposed. For a homogeneous sea with arbitrary inherent optical properties this equation is solved analytically. For an inhomogeneous sea it is solved approximately for any arbitrary stratification. The resulting equation expresses the diffuse reflection coefficient of the sea through vertica...

We consider a splitting-based approximation of the abstract differential Riccati equation in the setting of Hilbert–Schmidt operators. The Riccati equation arises in many different areas and is important within the field of optimal control. In this paper we conduct a temporal error analysis and prove that the splitting method converges with the same order as the implicit Euler scheme, under the...