To solve the MIQP estimation problem in real-time, various steps are taken to
minimize the time needed for calculation [8]. The type of constraints
in this propositional logic problem allow significant improvement in the solution
time. In a situation where F disturbances are possible and the system
is constrained to allow only a single disturbance, S=1, the problem reduces
significantly. A small-scale quadratic programming problem can be solved for
each of the F disturbances. Because the faults are mutually exclusive,
this can easily be accomplished. This procedure must take into account the effect
of previous solutions in order to be accurate. If fault
were
found to be optimal at time k , the objective function at time k+1for all other disturbances must show a cost for changing the values for
to zero across the horizon.
Decomposing the MIQP solution into multiple small scale QP problems allows for the use of computing power in parallel. The separate QP optimization problems can be solved using computational processes on separate CPUs, potentially even in different machines. The QP solution processes can also be warm started by using the solutions from the previous time step to warm start the QP calculation.
