Control of large-scale dynamic systems by aggregation
TL;DR: 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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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.
Abstract: This paper surveys the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems.
1,124 citations
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.
433 citations
Book•
01 Jan 1992
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.
Abstract: Large scale control systems results of multivariable feedback systems models and structure of interconnected systems decentralized stabilizability the decentralized stabilization and pole assignment optimal decentralized control stability analysis of interconnected systems decentralized design for strongly coupled subsystems decentralized design for weakly coupled systems decentralized PI controllers strongly coupled symmetric composite systems survey of the results and open problems in feedback control of large-scale systems.
427 citations
01 Oct 1976
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.
Abstract: For systems with slow and fast subsystems a near-optimum state regulator is composed of two subsystem regulators. Conditions for complete separation of slow and fast regulator designs are formulated. A second order approximation of the optimal performance is achieved without the Knowledge of the small singular perturbation parameter.
312 citations
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.
Abstract: 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. This form of the necessary conditions considerably simplifies previous results of Wilson [1] and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of Moore [2]. The possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation-type algorithm is proposed for computing these local extrema. A component-cost analysis of the model-error criterion similar to the approach of Skelton [3] is utilized at each iteration to direct the algorithm to the global minimum.
260 citations
References
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12 citations
TL;DR: Both finite-and infinite-dimensional, linear, time-invariant systems are characterized and application to Cauchy problems and distribution semigroups is presented.
10 citations
Journal Article•
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TL;DR: An attempt is made here to lay foundations for a control theory based on a plan of attack utilized by human organizations for centuries; namely, notions of division of labor and co-ordination.
Abstract: The optimal control of complex multivariable systems poses a great many problems for the control engineer. Among the most difficult of these is the computational problem. An attempt is made here to lay foundations for a control theory based on a plan of attack utilized by human organizations for centuries; namely, notions of division of labor and co-ordination. The usefulness of these concepts is examined via a number of mathematical models.
9 citations
TL;DR: The determinant equality known in linear algebra is shown to be an effective tool for control engineers in reducing complexity of eigenvalue computation and increasing insight into system behavior as discussed by the authors, and its applications to matrix products and singular matrices, to the study of systems with poles at the origin, and to the problem of finding the characteristic equation of an optimal regulator problem.
Abstract: A determinant equality known in linear algebra is shown to be an effective tool for control engineers in reducing complexity of eigenvalue computation and increasing insight into system behavior. Included are its applications to matrix products and singular matrices, to the study of systems with poles at the origin, and to the problem of finding the characteristic equation of an optimal regulator problem.
9 citations