Nils R. Sandell

Survey of decentralized control methods for large scale systems

This paper surveys the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems.

Detection with distributed sensors

The extension of classical detection theory to the case of distributed sensors is discussed, based on the theory of statistical hypothesis testing. The development is based on the formulation of a decentralized or team hypothesis testing problem. Theoretical results concerning the form of the optimal decision rule, examples, application to data fusion, and open problems are presented.

Robustness results in linear-quadratic Gaussian based multivariable control designs

The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity. In particular, robustness results associated with multivariable control systems designed on the basis of linear-quadratic (LQ) and the linear-quadratic Gaussian (LQG) design methodologies are presented.

On the numerical solution of the discrete-time algebraic Riccati equation

In this paper we shall present two new algorithms for solution of the diserete-time algebraic Riccati equation. These algorithms are related to Potters and to Laubs methods, but are based on the solution of a generalized rather than an ordinary eigenvalue problem. The key feature of the new algorithms is that the system transition matrix need not be inverted. Thus, the numerical problems associated with an ill-conditioned transition matrix do not arise and, moreover, the algorithm is directly applicable to problems with a singular transition matrix. Such problems arise commonly in practice when a continuous-time system with time delays is sampled.

Solution of some nonclassical LQG stochastic decision problems

This paper considers stochastic problems in team theory. In particular, the linearity of the optimal control laws for the one-step delay linear quadratic Gaussian (LQG) stochastic control problem is established, and explicit formulae are presented. In addition, the control sharing, nonstatic, nonclassical LQG problem is solved.

Solution of Large-Scale Optimal Unit Commitment Problems

This paper is concerned with the solution of large-scale unit commitment problems. An optimization model has been developed for these problems that incorporates minimum up and down time constraints, demand and reserve constraints, cooling-time dependent startup-costs, and time varying shutdown costs, as well as other practical considerations. A solution methodology has been developed for the optimization model that has two unique features. First, computational requirements grow only linearly with the number of units. Second, performance of the algorithm can be shown (rigorously) to actually improve as the number of units increases. With a preliminary computer implementation of the algorithm, we have been able to reliably solve problems with 250 units over 12 (2-hour) time periods, and we expect to be able to easily double these numbers.

Brief paper: Robust stability of systems with application to singular perturbations

In this paper we will give a simple approach to determining conditions for stability of feedback systems subject to perturbations in the operators describing these systems. The approach is based on techniques used in functional analysis, and provides an alternative development and generalization of some conditions for the linear time-invariant case that have appeared in the literature very recently. As an example of the application of the conditions, we consider the determination of finite regions of stability for singularly perturbed systems.

A tracking filter for maneuvering sources

It is well known that the extended Kalman filtering methodology works well in situations characterized by a high signal-to-noise ratio, good observability and a valid state trajectory for linearization. This paper considers a problem not characterized by these favorable conditions. A large number of ad hoc modifications are required to prevent divergence, resulting in a rather complex filter. However, performance is quite good as judged by comparison of Monte Carlo simulations with the Cramer-Rao lower bound, and by the filters ability to track maneuvering targets.

Robustness and modeling error characterization

The results on robustness theory presented here are extensions of those given in [1]. The basic innovation in these new results is that they utilize minimal additional information about the structure of the modeling error as well as its magnitude to assess the robustness of feedback systems for which robustness tests based on the magnitude of modeling error alone are inconclusive.

On the fixed-interval smoothing problem †

After a review of the development of the Mayne-Fraser two-filter smoother, a first principle argument is used to rederive this smoother. Reversed-time Markov models play a key role in forming a state estimate from future observations. The built-in asymmetry of the Mayne-Fraser smoother is pointed out, and it is shown how this asymmetry may be removed. Additionally, a covariance analysis of the two-filter smoother is provided, and reduced-order smoothers are analyzed.