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.read more
Citations
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Journal ArticleDOI
Weak connections, time scales, and aggregation of nonlinear systems
G. Peponides,Petar V. Kokotovic +1 more
TL;DR: If nonlinear subsystems with continuous equilibria are weakly connected, their local behavior is fast compared with the system-wide behavior caused by the connections, and an aggregate model which appears as a slow subsystem in the singular perturbation form of the model is described.
Journal ArticleDOI
Linear dynamics for the state vector of Markov chain functions
TL;DR: In this paper, the authors investigated under which conditions the random variable $(X_n)$ have the same distribution as a Markov chain with fixed transition probability matrix (for every n), and showed that the set of all probability distributions of a random variable such that it is weakly lumpable for the state vector can be finitely generated.
Proceedings ArticleDOI
Control of large decentralized dynamic systems
TL;DR: The nature of information flow in arriving at optimal control signals is examined for decentralized linear dynamic systems with local and supervisory controllers for problems with quadratic cost subject to terminal (target) state constraint.
Journal ArticleDOI
Random aggregation of univariate and multivariate linear processes
TL;DR: This paper derives second-order characteristics of random aggregate models of multivariate autoregressive moving-average processes and shows that random aggregation preserves the ARMA structure.
References
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Journal ArticleDOI
Decomposition Principle for Linear Programs
George B. Dantzig,Philip Wolfe +1 more
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
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"
M. Chidambara,Edward J. Davison +1 more
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.