  This paper presents a new robust data-driven predictive control scheme for
unknown linear time-invariant systems by using input-state-output or
input-output data based on whether the state is measurable. To remove the need
for the persistently exciting (PE) condition of a sufficiently high order on
pre-collected data, a set containing all systems capable of generating such
data is constructed. Then, at each time step, an upper bound of a given
objective function is derived for all systems in the set, and a feedback
controller is designed to minimize this bound. The optimal control gain at each
time step is determined by solving a set of linear matrix inequalities. We
prove that if the synthesis problem is feasible at the initial time step, it
remains feasible for all future time steps. Unlike current data-driven
predictive control schemes based on behavioral system theory, our approach
requires less stringent conditions for the pre-collected data, facilitating
easier implementation. Further, the proposed predictive control scheme features
an infinite prediction horizon, potentially resulting in superior overall
control performance compared to existing methods with finite prediction
horizons. The effectiveness of our proposed methods is demonstrated through
application to an unknown and unstable batch reactor.
