  Recent years have witnessed a booming interest in data-driven control of
dynamical systems. However, the implicit data-driven output predictors are
vulnerable to uncertainty such as process disturbance and measurement noise,
causing unreliable predictions and unexpected control actions. In this brief,
we put forward a new data-driven approach to output prediction of stochastic
linear time-invariant (LTI) systems. By utilizing the innovation form, the
uncertainty in stochastic LTI systems is recast as innovations that can be
readily estimated from input-output data without knowing system matrices. In
this way, by applying the fundamental lemma to the innovation form, we propose
a new innovation-based data-driven output predictor (OP) of stochastic LTI
systems, which bypasses the need for identifying state-space matrices
explicitly and building a state estimator. The boundedness of the second moment
of prediction errors in closed-loop is established under mild conditions. The
proposed data-driven OP can be integrated into optimal control design for
better performance. Numerical simulations demonstrate the outperformance of the
proposed innovation-based methods in output prediction and control design over
existing formulations.
