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Start Over Subject Riccati equation

1. Hartman-Wintner type criteria for half-linear second order differential equations

Creator:
Pátíková, Zuzana
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
half-linear differential equation, Hartman-Wintner criterion, Riccati equation, and principal solution
Language:
English
Description:
We establish Hartman-Wintner type criteria for the half-linear second order differential equation r(t)Φ(x ′ ))′ + c(t)Φ(x) = 0, Φ(x) = |x| p−2 x, p > 1, where this equation is viewed as a perturbation of another equation of the same form.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability

Creator:
Ungureanu, Viorica Mariela
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Riccati equation, stochastic uniform observability, stabilizability, quadratic control, and tracking problem
Language:
English
Description:
In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential Riccati equation (BDRE) associated with these problems (see \cite {chen}, for finite dimensional stochastic equations or \cite {UC}, for infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see \cite {1990}, \cite {ukl}). Under stabilizability and uniform observability conditions and assuming that the control weight-costs are uniformly positive, we establish that BDRE has a unique, uniformly positive, bounded on ${\mathbf R}_{+}$ and stabilizing solution. Using this result we find the optimal control and the optimal cost. It is known \cite {ukl} that uniform observability does not imply detectability and consequently our results are different from those obtained under detectability conditions (see \cite {1990}).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public