Optimal controlled variables for polynomial systems

We present a method for finding optimal controlled variables, which are polynomial combinations of measurements. Controlling these variables gives optimal steady state operation. Our work extends the concept of self-optimizing control; starting from the first-order necessary optimality conditions, any unknown variables are eliminated using elimination theory for polynomial systems to obtain invariant variable combinations, which contain only known variables (measurements). If a disturbance causes the active constraints to change, the invariants may be used to identify, and switch to the right region. This makes the method applicable over a wide disturbance range with changing active sets. The procedure is applied to two case studies of continuous stirred tank reactors.

► Optimal steady state operation for polynomial systems.
► Polynomials in the measurements as controlled variables.
► Controlled variables equivalent to optimality conditions.
► Unmeasured disturbances eliminated from optimality conditions by sparse resultant.
► Controlled variables used to determine changes in the active set.