KAM: Automatic Planning and Interpretation of Numerical Experiments Using Geometrical Methods

KAM is a computer program that can automatically plan, monitor, and interpret numerical experiments with Hamiltonian systems with two degrees of freedom. The program has recently helped solve an open problem in hydrodynamics. Unlike other approaches to qualitative reasoning about physical system dynamics, KAM embodies a significant amount of knowledge about nonlinear dynamics. KAM's ability to control numerical experiments arises from the fact that it not only produces pictures for us to see, but also looks at (sic---in its mind's eye) the pictures it draws to guide its own actions. KAM is organized in three semantic levels: orbit recognition, phase space searching, and parameter space searching. Within each level spatial properties and relationships that are not explicitly represented in the initial representation are extracted by applying three operations ---(1) aggregation, (2) partition, and (3) classification--- iteratively.

Generative Temporal Planning with Complex Processes

Autonomous vehicles are increasingly being used in mission-critical applications, and robust methods are needed for controlling these inherently unreliable and complex systems. This thesis advocates the use of model-based programming, which allows mission designers to program autonomous missions at the level of a coach or wing commander. To support such a system, this thesis presents the Spock generative planner. To generate plans, Spock must be able to piece together vehicle commands and team tactics that have a complex behavior represented by concurrent processes. This is in contrast to traditional planners, whose operators represent simple atomic or durative actions. Spock represents operators using the RMPL language, which describes behaviors using parallel and sequential compositions of state and activity episodes. RMPL is useful for controlling mobile autonomous missions because it allows mission designers to quickly encode expressive activity models using object-oriented design methods and an intuitive set of activity combinators. Spock also is significant in that it uniformly represents operators and plan-space processes in terms of Temporal Plan Networks, which support temporal flexibility for robust plan execution. Finally, Spock is implemented as a forward progression optimal planner that walks monotonically forward through plan processes, closing any open conditions and resolving any conflicts. This thesis describes the Spock algorithm in detail, along with example problems and test results.

An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

Planning and Scheduling Decisions in Supply Chains with Multiple Supply Modes: An Integrated Approach

We address the problem of jointly determining shipment planning and scheduling decisions with the presence of multiple shipment modes. We consider long lead time, less expensive sea shipment mode, and short lead time but expensive air shipment modes. Existing research on multiple shipment modes largely address the short term scheduling decisions only. Motivated by an industrial problem where planning decisions are independent of the scheduling decisions, we investigate the benefits of integrating the two sets of decisions. We develop sequence of mathematical models to address the planning and scheduling decisions. Preliminary computational results indicate improved performance of the integrated approach over some of the existing policies used in real-life situations.