Using the S.Lie’s infinitesimal approach we establish the connection between integrability of a one-parameter family of the Riccati equations and the stationary KdV hierarchy. In this paper we will suggest a method for integrating a one-parameter family of the Riccati equations ux + u 2 = f(x, λ) (1) based on their Lie symmetries. Here f(x, λ) = λ + λVn−1(x) + · · ·+ λV1(x) + V0(x) and λ is an ...

State-dependent Riccati equation (SDRE) methods for designing control algorithms and observers for nonlinear processes entail the use of algebraic Riccati equations. These methods have yielded a number of impressive results, however, they can be computationally quite intensive and thus far they have not yielded to those attempting to assess their stability. This paper explores an alternative, t...

In this paper, a missile longitudinal autopilot is designed using a new nonlinear control synthesis technique (called theθ -D approximation). The particular D θ − methodology used in this paper is referred to as the D θ − 2 H design. The D θ − technique can achieve suboptimal solutions to a class of nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman (HJB)...

By means of Riccati transformation techniques, we establish some new oscillation criteria for the second order nonlinear dynamic equation

We prove a comparison theorem for the solutions of a rational matrix difference equation, generalizing the Riccati difference equation, and existence and convergence results for the solutions of this equation. Moreover we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing or almost stabilizing solution. AMS Classification: 39A10, 93E03.

It is shown that, under appropriate assumptions, the continuous algebraic Riccati equation with Toeplitz matrices as coefficients has Toeplitz-like solutions. Both infinite and sequences of finite Toeplitz matrices are considered, and also studied is the finite section method, which consists in approximating infinite systems by large finite truncations. The results are proved by translating the...

It is shown that the difference Riccati equation of the Stenlund–Gustafsson (SG) algorithm for estimation of linear regression models can be solved elementwise. Convergence estimates for the elements of the solution to the Riccati equation are provided, directly relating convergence rate to the signal-to-noise ratio in the regression model. It is demonstrated that the elements of the solution l...