Orthogonal Polynomial Bases for Data-Driven Analysis and Control of Continuous-Time Systems
Paolo Rapisarda, Henk J. van Waarde, M. Kanat Camlibel
Abstract
We use polynomial approximation theory to perform data-driven analysis and control of linear, continuous-time invariant systems. We transform the continuous-time input- and state trajectories into discrete sequences consisting of the coefficients of their orthogonal polynomial bases representations. We show that the dynamics of the transformed input- and state signals and those of the original continuous-time trajectories are described by the same system matrices. We investigate informativity, quadratic stabilization, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math></inline-formula> -performance problems for continuous-time systems. We deal with the case in which machine-precision accuracy in the representation of continuous-time signals can be achieved from the data using a finite number of basis elements, and the case in which the approximation error is non-negligible.