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Proceedings ArticleDOI

Optimal control of singularly perturbed time delay systems with an application to a coupled core nuclear reactor

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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.

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Citations
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Journal ArticleDOI

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.
Journal ArticleDOI

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.
Journal ArticleDOI

Singular perturbations in optimal control problems

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.
Journal ArticleDOI

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.
Journal ArticleDOI

H Control of Linear Singularly Perturbed Systems with Small State Delay

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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Contributions to the theory of optimal control

R. E. Kalman
TL;DR: In this article, the authors considered the problem of least square feedback control in a linear time-invariant system with n states, and proposed a solution based on the concept of controllability.
Journal ArticleDOI

The conjugate gradient method for optimal control problems

TL;DR: In this article, the authors extended the conjugate gradient minimization method of Fletcher and Reeves to optimal control problems, which is directly applicable only to unconstrained problems; if terminal conditions and inequality constraints are present, the problem must be converted to a non-constrained form; e.g., by penalty functions.
Journal ArticleDOI

Singular perturbation method for reducing the model order in optimal control design

TL;DR: In this paper, the optimal control for a high-order model of the plant is approximated by some functions obtained from two low-order models, the second being the sensitivity model.
Journal ArticleDOI

Asymptotic series solution of singularly perturbed optimal control problems

P. Sannuti
- 01 Mar 1974 - 
TL;DR: In this article, an explicit method of constructing an asymptotic power series solution of the TPBVP as the small parameter tends to zero is presented, which allows a separation of slow and fast dynamics in the problem while reducing the differential order of the equations.
Journal ArticleDOI

Asymptotic Expansions of Singularly Perturbed Quasi-Linear Optimal Systems

TL;DR: In this article, a class of two-point boundary value problems (TPBVPs) which arise in fixed final time free endpoint optimal control problems is considered, and an asymptotic power series solution of the TPBVP is constructed with respect to a parameter whose perturbation changes the differential order of the problem.
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