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A MULTI-RESOLUTION, PROBABILISTIC APPROACH TO TWO-DIMENSIONAL INVERSE CONDUCTIVITY PROBLEMS

SIGNAL PROCESSING 1989年第3期18卷 291-311页

作者： CHOU, KC WILLSKY, AS Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge MA 02139 U.S.A.

In this paper a method of estimating the conductivity in a bounded 2-D domain at multiple spatial resolutions given boundary excitations and measurements is presented. The problem is formulated as a maximum-likelihood estimation problem and an algorithm that consists of a sequence of estimates at successively finer scales is presented. By exploiting the structure of the physics, the problem at each scale is divided into two linear subproblems, each of which is solved using parallelizable relaxation schemes. The success of our algorithm on synthetic data is demonstrated and numerical results based on using the algorithm as a tool for exploring estimation performance is presented, as well as results based on using the algorithm to study the well-posedness of the problem, and the effects of fine-scale variations on coarse scale estimates. Examples based on analytical results that further the understanding of these issues are also presented. The results suggest the use of inhomogeneous spatial scales as a possible way of overcoming ill-posedness at points far away from the boundary. In dieser Arbeit stellen wir ein Verfahren zum Schätzen der Leitfähigkeit in einem abgeschlossenen zweidimensionalen Gebiet mit verschiedenen räumlichen Auflösungen bei gegebenen Randerregungen und -messungen vor. Wir formulieren das Problem als Maximum-Likelihood-Schätzproblem und geben einen Algorithmus an, der aus einer Folge von Schätzern auf immer kleiner werdenden Gittern besteht. Unter Ausnutzung der physikalischen Struktur haben wir das Problem auf jedem Gitter in zwei lineare Teilprobleme aufgeteilt, die jeweils mit Hilfe von parallelisierbaren Relaxationsverfahren gelöst werden. Wir wenden unseren Algorithmus erfolgreich auf synthetische Daten an und präsentieren numerische Ergebnisse, die auf dem Einsatz des Algorithmus als Hilfsmittel zur Untersuchung der Güte der Schätzung, der Gutartigkeit des Problems und der Auswirkungen von Variationen auf einem feineren Gitter auf den Schät

关键词： Multi-resolution maximum likelihood estimation partial differential equations Gauss-Seidel relaxation schemes Cramer-Rao bound

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TRANSPUTER control OF A FLEXIBLE ROBOT LINK

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MICROPROCESSORS AND MICROsystems 1989年第3期13卷 227-232页

作者： STAVENUITER, ACJ TERREEHORST, G BAKKERS, AWP Control Systems and Computer Engineering Laboratory Department of Electrical Engineering University of Twente PO Box 217 7500 AE Enschede The Netherlands

The applicability of transputers in control systems is investigated. This is done by implementing a controller for a flexible robot arm with one degree of freedom on a system consisting of an IBM-AT and four transputers. It is found that a control system with transputers offers a great improvement compared with conventional digital control systems. Transputers can solve the common problem in control practice, i.e. having very sophisticted controllers but not being able to implement them because they need too much computing time. However, transputers are not an optimal solution for more sophisticated control systems because of shortcomings in the scheduling mechanism.

关键词： control systems robots transputers

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Optimal solutions in weakly coupled multiple decision maker Markov chains with nonclassical information

Optimal solutions in weakly coupled multiple decision maker ...

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IEEE Conference on decision and control

作者： R. Srikant T. Basar Decision and Control Laboratory Department of Electrical and Computer Engineering and Coordinated Science Laboratory University of Illinois Urbana IL USA

For Markov chains controlled by a team of agents there is no generally applicable method for obtaining the optimal control policy if the delay in information sharing between the agents is more than one-step. the authors consider such a problem for a Markov chain whose transition probability matrix consists of blocks, with the coupling between the blocks being on the order of epsilon , where epsilon is a small parameter. It is shown that if each block is controlled by only one agent, then it is possible to obtain policies arbitrarily close to the optimal control policy by making use of the fact that the coupling between the blocks is weak. The authors present a complete set of results for the finite-horizon case and discuss possible extensions to the finite-horizon case.< >

关键词： Optimal control Delay Matrix decomposition Dynamic programming Stochastic processes Equations State-space methods

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A dynamic games approach to controller design: disturbance rejection in discrete time

A dynamic games approach to controller design: disturbance r...

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IEEE Conference on decision and control

作者： T. Basar Decision and Control Laboratory Coordinated Science Laboratory and the Department of Electrical and Computer Engineering University of Illinois Urbana IL USA

It is shown that the discrete-time disturbance-rejection problem, formulated in finite and infinite horizons, can be solved by making direct use of the available results on linear-quadratic zero-sum dynamic games. Under perfect state measurements the approach leads to a minimax controller which achieves the best performance bound, and also to a characterization of all linear controllers under which disturbance attenuation does not exceed a prescribed bound. For the former, the worst-case disturbance turns out to be a correlated random sequence with a discrete distribution, which means that the problem (viewed as a dynamic game between the controller and the disturbance) does not admit a pure-strategy saddle point. Also formulated is a stochastic version of the problem, where the disturbance is a partially stochastic process with fixed higher order moments (other than the mean). Here the minimix controller depends on the energy bound of the disturbance, provided that it is below a certain threshold. Several numerical studies are included to illustrate the main results.< >

关键词： control systems Minimax techniques Stochastic processes Time domain analysis Vectors Infinite horizon Attenuation measurement Riccati equations Random sequences control theory

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Distributed Relaxation-Type Algorithms for Noncooperative Games

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IFAC Proceedings Volumes 1989年第5期22卷 13-18页

作者： T. Başar Decision and Control Laboratory Coordinated Science Laboratory and the Department of Electrical and Computer Engineering University of Illionis 1101W Springfield Avenue Urbana IL 61801 USA

The main objective of this paper is to review some recent results and also to present some new algorithms for the on-line, distributed computation of equilibria in noncooperative deterministic and stochastic games. The algorithms to be studied are of the relaxation-type , which require memory on either the past policy choices or the past actions of the players, depending on whether the iteration (and learning) is in the policy or the action space. Our earlier work on this topic has shown that incorporating memory into Jacobi and Gauss-Seidel type iterations in two-person Nash games could lead to considerable improvements in both the region of convergence and the speed of convergence towards noncooperative equilibrium. under both asynchronous and totally asynchronous modes of update. The present paper shows that these appealing features carry over to partially asynchronous modes of update, when there is a bound on the memory available to one or more players. The paper also discusses robustness of the partially asynchronous relaxation-type algorithms to inaccuracies in each player's knowledge regarding the others' response functions.

关键词： Noncooperative games distributed computation robustness Nash equilibrium

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Time-varying vs. time-invariant compensation for rejection of persistent bounded disturbances and robust stabilization

Time-varying vs. time-invariant compensation for rejection o...

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IEEE Conference on decision and control

作者： J.S. Shamma M.A. Dahleh Department of Electrical Engineering and Computer Science Laboratory of Information and Decision Systems Massachusetts Institute of Technology Cambridge MA USA

Summary form only given, as follows. Consideration is given to time-varying compensation for linear time-invariant discrete-time plants subject to persistent bounded disturbances. In the context of certain feedback objectives, it is shown that time-varying compensation offers no advantage over time-invariant compensation. These results complement similar results for feedback systems subject to finite-energy disturbances. It is shown that time-varying compensation does not improve the optimal rejection of persistent bounded disturbances. This result is obtained by exploiting a key observation that any time-varying compensator which yields a given degree of disturbance rejection must do so uniformly over time, thereby removing any advantage of time-variation. This key observation was used to show that time-varying compensation does not improve the optimal rejection of disturbances, regardless of the norm used to measure the disturbances. Thus, absolutely summable, finite-energy, or persistent bounded disturbances can be treated in the same manner. It is shown that time-varying compensation does not help in the bounded-input-bounded-output robust stabilization of time-invariant plants with unstructured uncertainty. It is thus also shown that the small-gain theorem is both necessary and sufficient for the bounded-input-bounded-output stability of certain linear time-varying plants subject to unstructured linear time-varying perturbations.

关键词： Robustness Feedback Laboratories Time varying systems Stability

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Communication complexity in distributed algebraic computation

Communication complexity in distributed algebraic computatio...

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IEEE Conference on decision and control

作者： Z.-Q. Luo J.N. Tsitsiklis Laboratory of Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge MA USA

Consideration is given to a situation in which two processors, P/sub 1/ and P/sub 2/, are to evaluate a collection of functions f/sub 1/, . . . f/sub s/ of two vector variables x, y under the assumption that processor P/sub 1/ (respectively, P/sub 2/) has access only to the value of the variable x (respectively, y) and the functional form of f/sub 1/,. . ., f/sub s/. Bounds on the communication complexity (the amount of information that has to be exchanged between the processors) are provided. An almost optimal bound is derived for the case of one-way communication when the functions are polynomials. Lower bounds for the case of two-way communication that improve on earlier bounds are also derived. As an application, the case in which x and y are n*n matrices and f(x,y) is a particular entry of the inverse of x+y is considered. Under a certain restriction on the class of allowed communication protocols, an Omega (n/sup 2/) lower bound is obtained. The results are based on certain tools from classical algebraic geometry and field extension theory.< >

关键词： Complexity theory Distributed computing Laboratories computer science Polynomials Geometry Access protocols

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Recursive and iterative estimation algorithms for multiresolution stochastic processes

Recursive and iterative estimation algorithms for multiresol...

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IEEE Conference on decision and control

作者： K.C. Chou A.S. Willsky A. Benveniste M. Basseville Department of Electrical Engineering and Computer Science Laboratory of Information and Decision Systems MIT Cambridge MA USA IRISA Campus Universitaire de Beaulieu Rennes France

A particular class of processes defined on dyadic trees is treated. Three algorithms are given for optimal estimation/reconstruction for such processes: one reminiscent of the Laplacian pyramid and making efficient use of Haar transforms, a second that is iterative in nature and can be viewed as a multigrid relaxation algorithm, and a third that represents an extension of the Rauch-Tung-Striebel algorithm to processes on dyadic trees. The last involves a discrete Riccati equation, which in this case has three steps: prediction, merging and measurement update. Related work and extensions are briefly discussed.< >

关键词： Recursive estimation Iterative algorithms Stochastic processes Signal processing Multiresolution analysis Wavelet transforms Laplace equations Riccati equations Signal resolution computer science

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Limited-angel tomography using constrained sinogram restoration

Limited-angel tomography using constrained sinogram restorat...

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Multidimensional Signal Processing Workshop

作者： J.L. Prince A.S. Willsky Laboratory for Information and Decision Systems Massachusetts Institute of Technology Cambridge MA USA Department of Electrical and Computer Engineering Johns Hopkins University Baltimore MD USA

Summary form only given. An algorithm that calculates the maximum a posteriori estimate of the complete sinogram has been developed. It uses prior knowledge of the smoothness of the sinogram, fundamental mathematical constraints on the Radon transform, and a complete probabilistic characterization of the observation noise. The object is reconstructed using convolution backprojection applied to the restored sinogram. The observation that many objects of interest tend to have smooth sinograms, although the objects themselves may not be smooth, has been incorporated by defining a Markov random field prior probability on full sinograms, rather than on objects. The Markov random field used is of the simplest kind-nearest neighbor with quadratic potential terms-although more elaborate models can be used. Using a known noise model (zero-mean, Gaussian), the maximum a posteriori solution to the sinogram restoration problem can be formulated. The solution to this problem is a constrained optimization algorithm, and because of the simple form of both the prior and the observation noise, it was possible to develop an iterative primal-dual algorithm that converges quite rapidly too the desired solution.< >

关键词： Tomography Image restoration Markov random fields Image reconstruction Iterative algorithms Laboratories Biomedical imaging Sonar Reconstruction algorithms Maximum a posteriori estimation

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Optimum Algebraic Design of Continuous-Time Regulators with Polyhedral Constraints

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IFAC Proceedings Volumes 1989年第6期22卷 291-294页

作者： M. Vassilaki G. Bitsoris AMBER S.A.Computer Systems POB3500 Athens.Greece Control Systems Laboratory.Electrical Engineering Department University of patras 26500 Patras Greere

In this paper, the Linear Constrained Regulation Problem for continuous-time systems will be studied and a design algorithm for a linear constrained feedback controller will be developed. Both state and control vectors are assumed to be subjected to linear constraints The approach presented, is based on the notion of positive invariance of polyhedral sets. Existence conditions for a control law that transfers asymptotically to the origin all initial states in a polyhedral subset of the state space is formulated. Then, a solution to the LCRP is derived solving a non-linear optimization problem

关键词： Linear systems stability positively invariant sets optimisation

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