Data-driven SISO predictive control using adaptive discrete-time fliess operator approximations

Modern control theory has been applied successfully in a wide variety of engineering disciplines for decades. In sharp contrast to this situation, however, there are fields like ecology where control methodologies have not been so successful in practice. This largely due to the poor quality of models that are available and the limited amount of reliable data that can be gathered. An emerging set of control techniques known collectively as data-driven control appears to be a natural candidate for control problems in such fields. The main objective of this paper is to describe one such algorithm based on recent advances in the modeling of nonlinear input-output systems in terms of Chen-Fliess series or Fliess operators. The idea is to combine a class of discrete-time Fliess operator approximators with a standard least-squares algorithm found in adaptive control to produce a time-varying input-output model that can be used to do predictive control. As an illustration, the method is applied to a predator-prey model in order to control the population level of the prey species.