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We will furthermore choose to express the corrective control forces, DU_i^*, as the linear sum of

several "basis" corrective actions:

U^nomN
+_[!]k_ijDU_j
j=1

U^nom+K_i* DU

U_i

=

=

(3.4)

where [!]U_jare fixed control perturbations which are defined over a cycle and k_ijare linear scaling

factors applied to [!]U_j. K_iis the vector of perturbation scaling factors and [!]U is a vector whose

elements are the fixed control perturbations, [!]U_j, which remain the same from one cycle to the

next. Nis the dimensionality of our control system and is equal to the number of state variables

which we wish to observe (and control).

Rather than using the complete system state, we choose to work with a small number of regulation

variables(RVs).

Regulation variables are a projection of the system state and are the observed