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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

Simulation relations for discrete-time linear systems

TL;DR: This paper establishes and characterize simulation relations for arbitrary discrete-time, linear control systems and considers various embeddings into labeled transition systems, that differ in the amount of timing information that is maintained in the transition relation.
Journal ArticleDOI

A Canonical Form for the Inclusion Principle of Dynamic Systems

TL;DR: This work will derive a canonical form for larger systems (expansions) that are obtained by expanding smaller systems (contractions) and propose an explicit characterization of contractible control laws subject to overlapping information structure constraints.
Journal ArticleDOI

Impulse energy approximation of higher-order interval systems using Kharitonov’s polynomials:

TL;DR: In this paper, the reduced-order interval numerator and denominator polynomials are determined by using Kharitonov's polynomial and a general form of the Routh approximation method.
Proceedings Article

An Introduction to Markov Modeling: Concepts and Uses

TL;DR: This tutorial addresses the need to answer more basic questions regarding Kharkov modeling: what are the capabilities and limitations of Kharksov modeling as a modeling technique?

Order Reduction of Linear Interval Systems Using Genetic Algorithm

TL;DR: In this algorithm the numerator and denominator polynomials are determined by minimizing the Integral square error using genetic algorithm (GA), which is simple, rugged and computer oriented.
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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