Sliding‐horizon optimal and certainty‐equivalent controllers for stabilizing stochastic‐parameter systems

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Abstract
This paper introduces novel control schemes to stabilize linear discrete stochastic‐parameter systems. It is shown that under some mild conditions, controllers that are optimal in the sense of minimizing a finite sliding‐horizon performance index subject to linear stochastic‐parameter system constraint are stabilizing for the system in both senses of almost‐sure and mean‐square asymptotic stability. Moreover, if the uncertainties of stochastic parameters are small enough, the designer can even stabilize these systems by the use of controllers that are designed on the basis of the deterministic equivalent of these systems.