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.
Citations
More filters
01 Aug 1999
TL;DR: This paper presents a method of reduction for interval system using the concept of interlacing property of even and odd polynomials of the system denominator to obtain the denominator of the reduced model.
Abstract: This paper presents a method of reduction for interval system. The denominator of the reduced model is obtained by using the concept of interlacing property of even and odd polynomials of the system denomiator. The numerator of the reduced model is obtained by matching interval time moments. A numerical example illustrates the procedure.
1 citations
07 Dec 1988
TL;DR: In this paper, a model-order reduction procedure for gas distribution networks is proposed to facilitate simulation and control system design studies, and the model is validated against test result data, and a final reduction procedure is applied at this stage to give a control system that can be implemented on a PC.
Abstract: A modeling technique has been developed for gas distribution networks which includes a model-order-reduction procedure to facilitate simulation and control system design studies. The model is validated against test result data. The effect of the model-reduction procedure is to introduce uncertainties into the model, and the implications of the uncertainties are investigated in relation to control system design. The design results in a high-order controller, and a final reduction procedure is applied at this stage to give a control system that can be implemented on a PC. >
1 citations
28 Jul 2015
TL;DR: A new approach of hierarchical control design for nonlinear systems is discussed based on the notion of approximate simulation relation recently introduced and a method to design the interface and simulation function by feedback linearization is presented.
Abstract: Hierarchical control method imposing a two-layer hierarchical structure on the control system architecture is a recently developed method for the investigation of system properties and the design of control laws. This method is fully worthy of being studied because of the powerful forces it shows in complex dynamics, especially large-scale systems. In this paper, a new approach of hierarchical control design for nonlinear systems is discussed based on the notion of approximate simulation relation recently introduced. Then we present a method to design the interface and simulation function by feedback linearization.
1 citations
01 Jan 2008
TL;DR: A broad survey of the proper modeling literature is presented, with the intention of helping the modeler to identify the most suitable proper modeling method for a given application.
Abstract: A dynamic system model is proper for a particular application if it achieves the accuracyrequired by the application with minimal complexity. Because model complexity often—but not always—correlates inversely with simulation speed, a proper model is oftenalternatively defined as one balancing accuracy and speed. Such balancing is crucial forapplications requiring both model accuracy and speed, such as system optimization andhardware-in-the-loop simulation. Furthermore, the simplicity of proper models conducesto control system analysis and design, particularly given the ease with which lower-ordercontrollers can be implemented compared to higher-order ones. The literature presentsmany algorithms for deducing proper models from simpler ones or reducing complexmodels until they become proper. This paper presents a broad survey of the propermodeling literature. To simplify the presentation, the algorithms are classified into fre-quency, projection, optimization, and energy based, based on the metrics they use forobtaining proper models. The basic mechanics, properties, advantages, and limitations ofthe methods are discussed, along with the relationships between different techniques, withthe intention of helping the modeler to identify the most suitable proper modeling methodfor a given application.
1 citations
1 citations
References
More filters
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.
Abstract: 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. The coordinating program generates at each cycle new objective forms for each part, and each part generates in turn from its optimal basic feasible solutions new activities columns for the interconnecting program. Viewed as an instance of a “generalized programming problem” whose columns are drawn freely from given convex sets, such a problem can be studied by an appropriate generalization of the duality theorem for linear programming, which permits a sharp distinction to be made between those constraints that pertain only to a part of the problem and those that connect its parts. This leads to a generalization of the Simplex Algorithm, for which the decomposition procedure becomes a special case. Besides holding promise for the efficient computation of large-scale systems, the principle yields a certain rationale for the “decentralized decision process” in the theory of the firm. Formally the prices generated by the coordinating program cause the manager of each part to look for a “pure” sub-program analogue of pure strategy in game theory, which he proposes to the coordinator as best he can do. The coordinator finds the optimum “mix” of pure sub-programs using new proposals and earlier ones consistent with over-all demands and supply, and thereby generates new prices that again generates new proposals by each of the parts, etc. The iterative process is finite.
2,281 citations
01 Jan 1960
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.
Abstract: THIS is one of the two ground-breaking papers by Kalman that appeared in 1960—with the other one (discussed next) being the filtering and prediction paper. This first paper, which deals with linear-quadratic feedback control, set the stage for what came to be known as LQR (Linear-Quadratic-Regulator) control, while the combination of the two papers formed the basis for LQG (Linear-Quadratic-Gaussian) control. Both LQR and LQG control had major influence on researchers, teachers, and practitioners of control in the decades that followed. The idea of designing a feedback controller such that the integral of the square of tracking error is minimized was first proposed by Wiener [17] and Hall [8], and further developed in the influential book by Newton, Gould and Kaiser [12]. However, the problem formulation in this book remained unsatisfactory from a mathematical point of view, but, more importantly, the algorithms obtained allowed application only to rather low order systems and were thus of limited value. This is not surprising since it basically took until theH2-interpretation in the 1980s of LQG control before a satisfactory formulation of least squares feedback control design was obtained. Kalman’s formulation in terms of finding the least squares control that evolves from an arbitrary initial state is a precise formulation of the optimal least squares transient control problem. The paper introduced the very important notion of c ntrollability, as the possibility of transfering any initial state to zero by a suitable control action. It includes the necessary and sufficient condition for controllability in terms of the positive definiteness of the Controllability Grammian, and the fact that the linear time-invariant system withn states,
1,451 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: 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.
Abstract: The paper presents 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. The estimator reconstructs the state vector exactly for deterministic systems while the steady-state performance in the stochastic case may be comparable to that obtained by the optimal (unconstrained) Wiener-Kalman filter.
68 citations
67 citations