DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

Manuscript for IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 4
solution) and (plan) completion time. These two metrics directly affect the performance of the
operation.
In this paper we design a control mechanism for such novel networks. We stress scalability
with respect to computational complexity as well as communicational overhead, as an important
consideration of the control mechanism for its practical use. The control mechanism should be
able to supply appropriate control policy in a timely manner even though the size of the network
is large. Such a property is important especially when completion time is an explicit
consideration as in our control problem. However, the property is hard to achieve in general if
one pursues exactly optimal policy. Therefore, we design a scalable control mechanism by
sacrificing some amount of optimality in a systematic way as follows.
First, we adopt Model Predictive Control (MPC) as our control framework. In MPC, for each
current state, an optimal open-loop control policy is designed for finite-time horizon by solving a
static mathematical programming model [10]-[13]. The design process is repeated for the next
observed state feedback forming a closed-loop policy reactive to each current system state.
Though MPC does not give absolutely optimal policy in stochastic environments, the periodic
design process alleviates the impacts of stochasticity. Note that technologies such as Dynamic
Programming are not efficient in terms of computational complexity as they try to give optimal
closed-loop control policy. Second, under MPC framework, we build a heuristic programming
model due to computational complexity. The heuristic model is solvable in polynomial time and
its solution converges to the solution of exact model in the limit of large number of tasks. Third,
we provide a decentralized coordination mechanism for solving the programming model.
Computations and communications are distributed to multiple entities through an auction market
while giving a solution equivalent to the solution of the programming model.