Journal ArticleDOI
The asymptotic behaviour of attainable sets of singularly-perturbed linear autonomous control systems☆☆☆
A.I. Ovseyevich,T.Yu. Figurina +1 more
TLDR
In this article, the asymptotic properties of attainable sets of singularly-perturbed linear autonomous control systems are investigated and it is shown that if an explicitly given linear scaling operator is applied to the attainable set, the resulting sets converge (as the small parameter tends to zero).About:
This article is published in Journal of Applied Mathematics and Mechanics.The article was published on 1998-01-01. It has received 3 citations till now. The article focuses on the topics: Asymptotic analysis & Asymptotology.read more
Citations
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Journal ArticleDOI
Asymptotics of reachable sets of linear dynamical systems with impulsive control
TL;DR: The reachable sets of linear dynamical systems with constraints on the total impulse of control action under different assumptions concerning the spectrum of the system's matrix are obtained in this paper. But the reachable set can be represented in the form of the product of the scaling matrix and the normalized set, where the matrix is an elementary function of time.
Book ChapterDOI
Asymptotics for singularly perturbed reachable sets
TL;DR: Under an extra smoothness assumption, the coefficient of elog1/e is found in the asymptotics of the support function of the reachable set of singularly perturbed linear control systems.
Journal Article
Controllability and time-optimal control of systems with slow and fast modes.
Petar V. Kokotovic,A.H. Haddad +1 more
TL;DR: In this article, the controllability of linear systems with large and small time constants (singularly perturbed systems) is established, and the time-optimal control of such systems is shown to be separable into two time scales related to the slow and fast modes of the system.
References
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Journal ArticleDOI
Controllability and time-optimal control of systems with slow and fast modes
Petar V. Kokotovic,A.H. Haddad +1 more
TL;DR: The controllability of linear systems with large and small time constants (singularly perturbed systems) is established and the time-optimal control is shown to be separable into two time scales related to the slow and fast modes of the system.
Journal ArticleDOI
Singular Perturbation in Mayer’s Problem for Linear Systems
TL;DR: In this article, the convergence of the optimal control when the parameter tends to zero is analyzed for a linear system with a small parameter in the derivatives and constrained controls, and the state constrained case is discussed.
Journal ArticleDOI
On the controllability of singularly perturbed systems
TL;DR: In this paper, sufficient conditions for controllability of high-order systems of singularly perturbed type are formulated in terms of two lower-order subsystems, and the results are extended to a class of nonlinear systems.