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Journal ArticleDOI

Control of large-scale dynamic systems by aggregation

TLDR
Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived and questions of performance degradation and of stability of such suboptimally controlled systems are answered.
Abstract
A method is proposed to obtain a model of a dynamic system with a state vector of high dimension. The model is derived by "aggregating" the original system state vector into a lower-dimensional vector. Some properties of the aggregation method are investigated in the paper. The concept of aggregation, a generalization of that of projection, is related to that of state vector partition and is useful not only in building a model of reduced dimension, but also in unifying several topics in the control theory such as regulators with incomplete state feedback, characteristic value computations, model controls, and bounds on the solution of the matrix Riccati equations, etc. Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived. Questions of performance degradation and of stability of such suboptimally controlled systems are also answered in the paper.

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Citations
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Journal ArticleDOI

Computer aided design of suboptimal lqg controller

TL;DR: An interactive software package for the design of a suboptimal controller is proposed and an example is included to establish the need for this package.
Journal ArticleDOI

Decentralized Suboptimal Approach to the Control of Large- Scale Systems@@@الوصول لحاكم لا مركزي شبه مثالي للأنظمة الكبيرة المقياس

TL;DR: In this article, the authors proposed the finite moving horizon (MH) technique for the suboptimal decentralized linear quadratic problems, which is based on a finite stage solution of the Riccati difference equation.
Proceedings ArticleDOI

Reduced order modelling and state estimation applied to gas distribution systems

TL;DR: In this article, a reduced order model for complex, multi-feed gas networks has been developed which is based on an aggregation procedure, and the reduced model is then used with an estimation scheme to determine the pressure distribution in the network from a limited number of measurements.
Journal ArticleDOI

Entwurf eines Teilzustandsreglers mit Hilfe der Ordnungsreduktion / Design of a partial state feedback controller using order reduction

H. Roth
TL;DR: In this article, an explicite analytically closed and unique solution for the desired partial state feedback controller is obtained, which uses only a part of the state vector for feedback.
Proceedings ArticleDOI

Optimal Control Design of Large Scale Systems with Uncertainty

TL;DR: Developing a reduced order model and using it in the design procedure will alleviate the problem of large dimensions, and such design is used to obtain an approximate design for the full order system.
References
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Journal ArticleDOI

Decomposition Principle for Linear Programs

TL;DR: A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations.

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

On "A method for simplifying linear dynamic systems"

TL;DR: A method is proposed for reducing large matrices by constructing a matrix of lower order which has the same dominant eigenvalues and eigenvectors as the original system.
Journal ArticleDOI

Estimation of the state vector of a linear stochastic system with a constrained estimator

TL;DR: In this article, a constructive design procedure for the problem of estimating the state vector of a discrete-time linear stochastic system with time-invariant dynamics when certain constraints are imposed on the number of memory elements of the estimator is presented.
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