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DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

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Manuscript for IEEE Transactions on Automatic Control 9<br />

Stress<br />

Environment Modeling<br />

Sensor Design<br />

Sensor<br />

Component<br />

Sensor<br />

Component<br />

Sensor<br />

Component<br />

Mathematical<br />

Programming<br />

Periodic Auctioning<br />

Auction<br />

Decentralized<br />

Coordination<br />

Fig. 2. Overall control procedure<br />

5. Mathematical programming model<br />

In this section we define sensors <strong>and</strong> build a mathematical programming model under MPC<br />

framework.<br />

5.1 Sensors<br />

Each component monitors its operating environment through a sensor. The sensor measures<br />

resource availability MRA i (t), which is defined as available fraction of a resource when a<br />

component i requests that resource in the last control period at control point t. There are two<br />

quantities to extract this measurement, which are request time <strong>and</strong> execution time. Request time<br />

is the duration for which the component requests resource or equivalently queue length<br />

(including a task in service) is more than zero. Execution time is the duration for which the<br />

component utilizes the resource. If control period is SW, resource sensor calculates MRA i (t) as:

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