  For linear systems, many data-driven control methods rely on the behavioral
framework, using historical data of the system to predict the future
trajectories. However, measurement noise introduces errors in predictions. When
the noise is bounded, we propose a method for designing historical experiments
that enable the computation of an upper bound on the prediction error. This
approach allows us to formulate a minimax control problem where robust
constraint satisfaction is enforced. We derive an upper bound on the
suboptimality gap of the resulting control input sequence compared to optimal
control utilizing accurate measurements. As demonstrated in numerical
experiments, the solution derived by our method can achieve constraint
satisfaction and a small suboptimality gap despite the measurement noise.
