A decomposition of near-optimum regulators for systems with slow and fast modes
01 Oct 1976-Vol. 21, Iss: 5, pp 701-705
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.
Citations
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TL;DR: The survey is aimed at engineers and applied mathematicians interested in model-order reduction, separation of time scales and allied simplified methods of control system analysis and design.
539 citations
TL;DR: In this paper, the authors discuss typical applications of singular perturbation techniques to control problems in the last fifteen years and present a bibliography of more than 250 titles on the subject.
Abstract: This paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years. The first three sections are devoted to the standard model and its time-scale, stability and controllability properties. The next two sections deal with linear-quadratic optimal control and one with cheap (near-singular) control. Then the composite control and trajectory optimization are considered in two sections, and stochastic control in one section. The last section returns to the problem of modeling, this time in the context of large scale systems. The bibliography contains more than 250 titles.
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
TL;DR: In this paper, the authors considered the problem of approximate disturbance decoupling by measurement feedback and showed that this problem is solvable to any arbitrary degree of accuracy if and only if: 1) almost disturbance control by state feedback, and 2) approximate disturbance estimation of the to-be-controlled output are both possible.
Abstract: In Part I of this paper, almost controlled invariant subspaces were studied. In this part we will consider their duals, the almost conditionally invariant subspaces. These concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem. Finally, we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if: 1) almost disturbance decoupling by state feedback, and 2) almost disturbance decoupled estimation of the to-be-controlled output are both possible.
382 citations
TL;DR: In this article, a singular perturbation approach is used to unify a class of classical and recent results on high-gain systems and to show their relationships with multivariable transmission zero analysis, cheap control problems, and sliding mode in variable structure systems.
Abstract: In this paper a singular perturbation approach is used to unify a class of classical and recent results on high-gain systems and to show their relationships with multivariable transmission zero analysis, cheap control problems, and sliding mode in variable structure systems. A new pole placement method and a decomposition of near optimal high-gain regulator problems are presented.
366 citations
References
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TL;DR: The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.
892 citations
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.
Abstract: Often it is possible to represent physical systems by a number of simultaneous linear differential equations with constant coefficients, \dot{x} = Ax + r but for many processes (e.g., chemical plants, nuclear reactors), the order of the matrix A may be quite large, say 50×50, 100×100, or even 500×500. It is difficult to work with these large matrices and a means of approximating the system matrix by one of lower order is needed. A method is proposed for reducing such matrices by constructing a matrix of lower order which has the same dominant eigenvalues and eigenvectors as the original system.
614 citations
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.
505 citations
TL;DR: In this paper, a necessary and sufficient condition for the optimal control and filtering problem to yield an optimal asymptotically stable closed-loop system is given, which involves the concepts of stabilizability and detectability.
Abstract: The well-known matrix algebraic equation of the optimal control and filtering theory is considered. A necessary and sufficient condition for its solution to yield an optimal as well as asymptotically stable closed-loop system is given. The condition involves the concepts of stabilizability and detectability.
322 citations
TL;DR: The behavior of the Riccati equation for the linear regulator problem with a parameter whose perturbation changes the order of the system is analyzed in this article, where sufficient conditions are given under which the original problem tends to the solution of a low-order problem.
Abstract: The behavior of the solution of the Riccati equation for the linear regulator problem with a parameter whose perturbation changes the order of the system is analyzed. Sufficient conditions are given under which the solution of the original problem tends to the solution of a low-order problem. This result can be used for the decomposition of a high-order problem into two low-order problems.
210 citations