DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

Manuscript for IEEE Transactions on Automatic Control 6
tasks as well as tasks from predecessor components) and then sends it to successor components.
We denote the number of root tasks of component i as rt i . Fig. 1 shows an example network
composed of four components. Each of A 1 and A 2 has 100 root tasks. A 3 and A 4 have no root
tasks but they have 200 and 100 tasks respectively from the corresponding predecessors.
A 1
A 3
100
0
A 2 A 4
100
0
Fig. 1. An example network
3.2 Control action
A component can use one of alternative algorithms to process a task. Different alternatives
trade off CPU time and value of solution with more CPU time resulting in higher solution value.
As one can find optimal mixed alternatives, a component has a monotonically increasing convex
function, say value function, with CPU time as a function of value. We call the value in the
function as value mode that a component can select as its decision variable. A value function is
defined with three elements as
〈 f i ( vi
), vi(min),
vi(max)〉
as shown in Fig. 1. This function indicates
that component i’s expected CPU time 2 to process a task is f i (v i ) with a value mode v i and v i(min) ≤
v i ≤ v i(max) . We assume that components cannot change the mode for a task in process.
3.3 Stress environment
Survivability stresses such as malicious attacks and accidental failures, affect the system by
directly consuming resources or indirectly invoking defense mechanisms as remedies. For
2 The distribution of CPU time can be arbitrary though we use only expected CPU time.