Proceedings ArticleDOI
Optimal control of singularly perturbed time delay systems with an application to a coupled core nuclear reactor
Parvathareddy Reddy,Peddapullaiah Sannuti +1 more
- Vol. 13, pp 793-803
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TLDR
In this paper, an asymptotic power series solution of the optimal control of a class of high-order time delay systems is developed with respect to the scalar parameter, and the method is applied to an eighth order nonlinear time delay model of a coupled-core nuclear reactor system by reducing it to a second order ordinary model.Abstract:
Optimal control of a class of high-order time delay systems is considered. The mathematical description of these systems is written in such a way that whenever a scalar parameter is perturbed, the dimensionality of the system is reduced (singular perturbation). Further, the time delayed variables also will disappear from the system equations. An asymptotic power series solution of the optimal control is then developed with respect to the scalar parameter. This asymptotic control is valid for the high-order time delay system, while it is calculated on the basis of only a reduced order ordinary system. At first a scalar example illustrates the method of constructing the asymptotic expansions. Then the method is applied to an eighth order nonlinear time delay model of a coupled-core nuclear reactor system by reducing it to a second order ordinary model. Computationally, the asymptotic approximation method is compared with the second variation method and is shown to be superior.read more
Citations
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Asymptotic analysis and solution of a finite-horizon H∞ control problem for singularly-perturbed linear systems with small state delay
TL;DR: In this paper, a finite-horizon H∞ state-feedback control problem for singularly-perturbed linear time-dependent systems with a small state delay is considered.
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The linear quadratic optimal control problem for hereditary differential systems: Theory and numerical solution
TL;DR: In this paper, the optimal control problem for linear hereditary differential systems with a linear-quadratic cost function was studied and an approximation to the linear HDS in state form and the linear adjoint state equation was constructed and proved convergence.
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Singular perturbations in optimal control problems
A. B. Vasil'eva,M. G. Dmitriev +1 more
TL;DR: A survey of the works on the theory of optimal control by deterministic objects, described by systems of ordinary differential or difference equations, where the investigation is carried out with the aid of the methods of the singular perturbations is given in this paper.
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Asymptotic Solution of a Boundary-Value Problem for Linear Singularly-Perturbed Functional Differential Equations Arising in Optimal Control Theory
TL;DR: In this article, a formal asymptotic solution of the Hamiltonian boundary-value problem with delay in the state variables is proposed and the justification of this solution is done.
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H Control of Linear Singularly Perturbed Systems with Small State Delay
Valery Y. Glizer,Emilia Fridman +1 more
TL;DR: In this paper, an infinite horizon H∞ state-feedback control problem for singularly perturbed linear systems with a small state delay is considered, and a simplified controller with parameter-independent gain matrices, solving the original problem for all sufficiently small values of this parameter, is obtained.
References
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Petar V. Kokotovic,P. Sannuti +1 more
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Journal ArticleDOI
Asymptotic series solution of singularly perturbed optimal control problems
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