Designing Experiments for Data-Driven Control of Nonlinear Systems

In a recent paper we have shown that data collected from linear systems excited by persistently exciting inputs during low-complexity experiments, can be used to design state- and output-feedback controllers, including optimal Linear Quadratic Regulators (LQR), by solving linear matrix inequalities (LMI) and semidefinite programs. We have also shown how to stabilize in the first approximation unknown nonlinear systems using data. In contrast to the case of linear systems, however, in the case of nonlinear systems the conditions for learning a controller directly from data may not be fulfilled even when the data are collected in experiments performed using persistently exciting inputs. In this paper we show how to design experiments that lead to the fulfilment of these conditions.