  This article presents a performance analysis for stochastic predictive
control (SPC) in linear systems with quadratic performance index and additive
and multiplicative uncertainties. Under a finite support assumption, the
problem can be cast as a finite-dimensional quadratic program, but the problem
becomes quickly intractable as the problem size grows exponentially in the
horizon length. SPC aims to compute approximate solutions by solving a sequence
of problems with truncated prediction horizons and committing the solution in a
receding-horizon fashion. While this approach is widely used in practice, its
performance relative to the optimal solution is not well understood. This
article reports for the first time a rigorous performance guarantee of SPC:
Under stabilizability and detectability conditions, the dynamic regret of SPC
is exponentially small in the prediction horizon length, allowing SPC to
achieve near-optimal performance at a substantially reduced computational
expense.
