Controller design by symbolic regression

Abstract A novel method of empirical controller design is introduced with the potential to produce exotic controller forms. The controllers in this method are derived by symbolic regression (SR) to be in equation form, hence, they are legible in how the controller output is computed as a function of loop variables. Because SR is computationally costly due to its extensive search of controller space, requiring evaluation of millions, if not billions, of candidate controllers, the candidate controllers cannot be evaluated in closed-loop due to the high cost of simulation associated with such evaluation. This paper offers a recourse to this closed-loop evaluation by allowing evaluations to be performed algebraically. To this end, a method of inverse solution is introduced that estimates the plant input for a desired plant output. This estimated plant input is then used as the target output for candidate controllers that can be readily evaluated algebraically based on the available time series of loop variables associated with the desired plant output. Unlike traditional control design which relies on closed-loop performance metrics to provide controller performance guarantees, the proposed open-loop approach sacrifices such guarantees in favor of new controller forms that it may yield. Therefore, the fidelity, as controllers, of candidate controllers need to be verified post-design. For this purpose, the candidate controllers are first evaluated as controllers in closed-loop simulation. Once verified by simulation, they need to be validated for closed-loop stability, as demonstrated for one of the studied cases.