Journal ArticleDOI
Control of large-scale dynamic systems by aggregation
Reads0
Chats0
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
More filters
Journal ArticleDOI
Survey of decentralized control methods for large scale systems
TL;DR: In this article, the authors survey the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems, and present a survey of the control theory of large-scale systems.
Journal ArticleDOI
Criteria of asymptotic stability of differential and difference inclusions encountered in control theory
TL;DR: For a class of differential inclusions, to which many of the practically important control systems can be reduced, necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of Lyapunov functions.
Book
Feedback control of large-scale systems
TL;DR: A survey of the results and open problems in feedback control of large-scale systems of multivariable feedback systems and structure of interconnected systems.
Proceedings ArticleDOI
A decomposition of near-optimum regulators for systems with slow and fast modes
Joe H. Chow,Petar V. Kokotovic +1 more
TL;DR: In this article, conditions for complete separation of slow and fast regulator designs are formulated and a second order approximation of the optimal performance is achieved without the knowledge of the small singular perturbation parameter.
Journal ArticleDOI
The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore
TL;DR: In this paper, the first-order necessary conditions for quadratically optimal reduced-order modeling of linear time-invariant systems are derived in the form of a pair of modified Lyapunov equations coupled by an oblique projection which determines the optimal reduced order model.
References
More filters
Journal ArticleDOI
A class of suboptimal linear controls
TL;DR: In this paper, a suboptimal solution of the linear regulator problem is presented, which affords some computational simplicity over the optimal solution, and a linear first-order matrix differential equation whose solution gives the value of the performance index for the sub-optimal control is then derived.
Journal ArticleDOI
Transfer function representation of the aggregate behavior of a class of economic processes
TL;DR: The purpose of this paper is to describe certain techniques which have proved useful in the systems analysis of large scale economic systems and applications of the method are demonstrated with respect to problems arising in a system analysis of the U. S. plywood industry.
Journal ArticleDOI
An improved algorithm for the solution of discrete regulation problems
TL;DR: The characteristics of recently published canonical forms for controllable systems are exploited to reduce the number of free parameters appearing in the system matrices to derive a simply computed canonical form for the weighting matrix.
Journal ArticleDOI
Questions & Answers: Aggregation in Matrix Models of Resource Flows
Journal ArticleDOI
On the reticulation problem in multivariable control systems
TL;DR: In this article, the problem of reticulating (partitioning) a multivariable control problem is investigated and an iterative process is suggested, where each subprogram is solved successively under the conditions imposed by the solutions of the other subproblems through the interactions of the original control problem.