For related work on plantwide control see here

Self-optimizing control is related to selecting the right economic controlled variables (CVs) and by this to move more of the burden of economic optimization from the slower time scale of the real-time optimization layer (RTO) into the faster setpoint control layer. Ideally, the setpoint of self-optimizing variable is independent of disturbances, but this in practice some adjustment may be needed on a slower time scale. This discussion about reducing setpoint changes for CVs is related to the unconstrained degrees of freedom (for example, a trade-off between too much or too little recycle), but usually most of the CVs are active constraints where the setpoint is fixed by specifications (for example, a maximum allowed impurity in a product). One may view the active constraints and the "obvious self-optimizing variables", because it is clear that tight control of these variables (with a small back-off) provide more optimal operation. The active constraints may change depending on operation, and for this the conventional approach is to use selectors. The selector approach often works very well but it depends on selecting appropriate MV-CV pairings, and there may be more complex cases where centralized optimization (RTO) is needed. In todays situation with more renewable energy sources and more flexible operation, the self-optimizing approach has a large potential. Moving more of the optimization into the fast control layer, allows for much faster adjustment to changing conditions, for example, for cases where power prices vary and make it necessary to make frequent changes in operation. If the optimal setpoints of the unconstrained CVs vary, then one approach may be to use models (or data) to predetermine optimal setpoints as a function of expected disturbances, including price variations.

Second, we need to find controlled variables associated with the unconstrained degrees of freedom. These are the less obvious self-optimizing control variables. We are looking for some "magic" variables, which when kept constant, indirectly achieves optimal operation in spite of disturbances.

** "Self-optimizing control is when acceptable operation under all conditions is achieved with
constant setpoints for the controlled variables."
**

Here "acceptable operation" is more precisely defined by the value of the loss, and "under all conditions" means for the defined disturbances, plant changes and implementation errors.

To include biological system the term "self-optimizing control" should possibly be broadened further, for example, by replacing "with constant setpoints for the controlled variables" by "by controlling the right variables" or something similar.

The main issues in selecting controlled variables are disturbances and implementation error (noise, measurement error). All results below are based on a steady-state analysis, since the economics of most processes are determined mainly by the steady.state behavior, but the extension to batch processes (with optimal trajectories) is simple.

A survey of self-optimizing control was published in 2017:

A good introduction to self-optimizing control, with lots of simple examples, is the following paper:

An extremely simple method ("nullspace method") has been derived by Vidar Alstad which gives the optimal linear measurement combination c=Hy (with zero loss) for the case with no implementation error (i.e., noise free-case, n=0). It is briefly descibed in the first paper, and more details can be found here

The following paper applies the "brute-force approach" to the Tennessee-Eastman challenge problem and discusses in particular the feasibility issue (which, by the way, a local method will not detect)

The following paper discusses in more detail the issue of back-off and also shows that it is optimal in some cases - in particular to be feasible - to use "robust" setpoints rather than the nomically optiomal setpoints:

The following summary of the maximum gain rule may be useful: Pages from corrected version of book (July 2007)

The maximum gain rule has been applied to many examples. In particular, for scalar cases it is very simple (and efficient!) to use. For multivariable cases, maximizing the minimum singular value is usually OK, but it may fail for some ill-conditioned processes, like distillation: