Data-Driven Internal Model Control of Second-Order Discrete Volterra Systems

The increase in system complexity paired with a growing availability of operational data has motivated a change in the traditional control design paradigm. Instead of modeling the system by first principles and then proceeding with a (model-based) control design, the data-driven control paradigm proposes to directly characterize the controller from data. By exploiting a fundamental result of Willems and collaborators, this approach has been successfully applied to linear systems, yielding data-based formulas for many classical linear controllers. In the present paper, the data-driven approach is extended to a class of nonlinear systems, namely second-order discrete Volterra systems. Two main contributions are made for this class of systems. At first, we show that - under a necessary and sufficient condition on the input data excitation - a data-based system representation can be derived from input-output data and used to replace an explicit system model. That is, the fundamental result of Willems et al. is extended to this class of systems. Subsequently a data-driven internal model control formula for output-tracking is derived. The approach is illustrated via two simulation examples.