Combining Learning and Model Based Control: Case Study for Single-Input Lotka-Volterra System

A hybrid control architecture for nonlinear dynamical systems is described which combines the advantages of model based control with those of real-time learning. The basic idea is to generate input-output data from an error system involving the plant and a proposed model. A discretized Chen-Fliess functional series is then identified from this data and used in conjunction with the model for predictive control. This method builds on the authors' previous work on model-free control of a single-input, single-output Lotka-Volterra system. The problem is revisited here, but now with the introduction of a model for the dynamics. The single-input, multiple-output version of the problem is also investigated as a way to enhance closed-loop performance.