Results 191 to 200 of about 6,844 (227)

Singularly Perturbed Optimal Tracking Problem

Differential Equations
We consider a singularly perturbed optimal tracking problem with a given etalon trajectory in the case of incomplete information about the state vector in the presence of external disturbances. To analyze the differential equations that arise when solving this problem, the decomposition method is used, which is based on the technique of integral ...
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Interior Estimates for Singularly Perturbed Problems

Zeitschrift für Analysis und ihre Anwendungen, 1984
The solution of the Dirichlet problem for a singularly perturbed elliptic differential equation \epsilon L_1u + L_0u = h of order 2m converges, for
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Singularly Perturbed Operators

1994
Let A = A* > 1 be a self-adjoint unbounded operator in a separable complex Hilbert space H.
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On Invariant Manifolds in Singularly Perturbed Systems

Journal of Dynamical and Control Systems, 1999
The author deals with a slow-fast system \[ \dot x=f(x,y, \varepsilon), \quad \dot y=\varepsilon g(x,y, \varepsilon), \quad \dot\varepsilon=0 \] where \(x\in\mathbb{R}^\ell\), \(y\in\mathbb{R}^m\), \(\varepsilon\in \mathbb{R}\). Assuming that the fast system \(\dot x=f(x,y,0)\), \(\dot y=0\) has a compact smooth invariant manifold with boundary \(M_0 ...
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Asymptotics for Singularly Perturbed Reachable Sets

2010
We study, in the spirit of [1], reachable sets for singularly perturbed linear control systems The fast component of the phase vector is assumed to be governed by a strictly stable linear system It is shown in loc.cit that the reachable sets converge as the small parameter e tends to 0, and the rate of convergence is O(eα), where ...
Elena V. Goncharova, Alexander I. Ovseevich   +1 more
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Square Powers of Singularly Perturbed Operators

Mathematische Nachrichten, 1995
AbstractWe use the method of self‐adjoint extensions to define a self‐adjoint operator AT as the singular perturbation of a given self‐adjoint operator A by a singular operator T on a Hilbert space.We also find the structure of a singular operator Q such that the singular perturbation of A2 by Q satisfies (A2)Q = (AT)2. We obtain the explicit form of Q
Albeverio, Sergio, Karwowski, Witold, Koshmanenko, Vladimir   +2 more
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Discretization of the semilinear singularly perturbed problem

Nonlinear Analysis: Theory, Methods & Applications, 1997
The authors discuss the construction of a spline function for a class of singularly perturbed singular problems: \[ -\varepsilon^2 x^{2\alpha} u'' (x) + b(x,u)=0, \quad x \in (0,1), \quad u(0)=u(1)=0 \tag{1} \] with parameter \(\alpha \in [0, 0.5) \) and a perturbation parameter \(\varepsilon \in (0, \varepsilon_0 ]\), \(\varepsilon_0 \ll 1\).
Uzelac, Zorica, Surla, Katarina
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Relaxation in singularly perturbed control systems

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2004
When slow and fast motions are coupled in a singularly perturbed control system, the application of relaxed controls may be needed on several levels. There may be a need to relax the control affecting the slow and the fast motions and there may be a need to relax the fast flow itself, which serves as a control for the slowly dynamics.
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Synthesis of Linear, Singularly Perturbed Systems

Journal of Mathematical Sciences, 2001
In connection with control theory the typical problem of formation of the feedback providing prescribed characteristics of the performance and stability of a closed system is considered. A concept of exterior polynomial is introduced for a system of ordinary differential equations with small parameters.
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Singularly perturbed Chern–Simons theory

Journal of Mathematical Physics, 1990
The Chern–Simons theory of an SU(2) gauge theory in three dimensions is looked at from a perturbative point of view. The pure Chern–Simons action is generalized by adding a conventional Yang–Mills action term. This acts as a singular perturbation. The resulting theory has a moduli space containing that of the pure Chern–Simons version; for certain ...
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