David A. Castanon

Combining and updating of local estimates and regional maps along sets of one-dimensional tracks

In this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates, generated at different times, of the same process sample path. The first of these cases has applications in decentralized estimation, while the second has applications in updating maps of spatially-distributed random quantities given measurements along several tracks. The method of solution for the second problem uses the result of the first, and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields.

Rollout algorithms for stochastic scheduling problems

Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. In this paper we focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, with considerable savings in computation over optimal algorithms. We delineate circumstances under which the rollout algorithms are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics.

Approximate dynamic programming for sensor management

This paper studies the problem of dynamic scheduling of multi-mode sensor resources for the problem of classification of multiple unknown objects. Because of the uncertain nature of the object types, the problem is formulated as a partially observed Markov decision problem with a large state space. The paper describes a hierarchical algorithm approach for efficient solution of sensor scheduling problems with large numbers of objects, based on a combination of stochastic dynamic programming and nondifferentiable optimization techniques. The algorithm is illustrated with an application involving classification of 10,000 unknown objects.

Distributed estimation algorithms for nonlinear systems

In this paper, we consider the problem of combining the local conditional distributions of a random variable which have been generated by local observers having access to their private information. Sufficient statistics for the local distributions are communicated to a coordinator, who attempts to reconstruct the global centralized distribution using only the communicated statistics. We obtain a distributed processing algorithm which recovers exactly the centralized conditional distribution. The results can be applied in designing distributed hypothesis-testing algorithms for event-driven systems.

Continuous-membrane surface-micromachined silicon deformable mirror

The authors describe the development of a new type of micromachined device designed for use in correcting optical aberrations. A nine-element continuous deformable mirror was fabricated using surface micromachining. The electromechanical behavior of the deformable mirror was measured. A finite-difference model for predicting the mirror deflections was developed. In addition, novel fabrication techniques were developed to permit the production of nearly planar mirror surfaces.

Adaptive aggregation methods for infinite horizon dynamic programming

A class of iterative aggregation algorithms for solving infinite horizon dynamic programming problems is proposed. The idea is to interject aggregation iterations in the course of the usual successive approximation method. An important feature that sets this method apart from earlier ones is that the aggregate groups of states change adaptively from one aggregation iteration to the next, depending on the progress of the computation. This allows acceleration of convergence in difficult problems involving multiple-ergodic classes for which methods using fixed groups of aggregate states are ineffective. No knowledge of special problem structure is utilized by the algorithms. >

The auction algorithm for the transportation problem

The auction algorithm is a parallel relaxation method for solving the classical assignment problem. It resembles a competitive bidding process whereby unassigned persons bid simultaneously for objects, thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. This paper generalizes the auction algorithm to solve linear transportation problems. The idea is to convert the transportation problem into an assignment problem, and then to modify the auction algorithm to exploit the special structure of this problem. Computational results show that this modified version of the auction algorithm is very efficient for certain types of transportation problems.

A forward/reverse auction algorithm for asymmetric assignment problems

In this paper we consider the asymmetric assignment problem and we propose a new auction algorithm for its solution. The algorithm uses in a novel way the recently proposed idea of reverse auction, where, in addition to persons bidding for objects by raising their prices, we also have objects competing for persons by essentially offering discounts. In practice, the new algorithm apparently deals better with price wars than the currently existing auction algorithms. As a result, it tends to terminate substantially (and often dramatically) faster than its competitors.

A scattering framework for decentralized estimation problems

In this paper we develop a comprehensive framework for the study of decentralized estimation problems. This approach imbeds a decentralized estimation problem into an equivalent scattering problem, and makes use of the super-position principle to relate local and centralized estimates. Some decentralized filtering and smoothing algorithms are obtained for a simple estimation structure consisting of a central processor and of two local processors. The case when the local processors exchange some information is considered, as well as the case when the local state-space models differ from the central model.

Distributed algorithms for dynamic reassignment

In this paper, we consider the problem of task partitioning among members of a team of cooperating agents in response to discovery of new tasks or potential failures of some agents. We assume that information about new targets or agent failures is received by individual team members, and communicated asynchronously with delays to the rest of the team. These delays create potential differences in information across the team of agents. We describe an asynchronous approach to coordinating the team response, where individual agents compute modifications to assignments based on local information. We show that the asynchronous algorithms converge to the same optimal assignments in the presence of arbitrary finite communication delays as a centralized information approach. We extend the asynchronous protocol to the solution of a class of stochastic dynamic resource assignment problems, and show asynchronous convergence of the resulting algorithms. Simulations illustrate the delays in computing an optimal assignment of tasks in response to dynamic events.