Stabilizing Stochastic Predictive Control under Bernoulli Dropouts

TL;DR

This paper develops tractable, recursive controllers for stochastic linear systems with bounded controls, accounting for noise and packet dropouts, ensuring stability under various transmission protocols.

Contribution

It introduces three transmission protocols and an optimization-based control design that guarantees mean square boundedness despite stochastic noise and Bernoulli dropouts.

Findings

Controllers ensure mean square boundedness of states.

Proposed methods are applicable for any non-zero success probability.

The approach handles bounded controls and stochastic disturbances effectively.

Abstract

This article presents tractable and recursively feasible optimization-based controllers for stochastic linear systems with bounded controls. The stochastic noise in the plant is assumed to be additive, zero mean and fourth moment bounded, and the control values transmitted over an erasure channel. Three different transmission protocols are proposed having different requirements on the storage and computational facilities available at the actuator. We optimize a suitable stochastic cost function accounting for the effects of both the stochastic noise and the packet dropouts over affine saturated disturbance feedback policies. The proposed controllers ensure mean square boundedness of the states in closed-loop for all positive values of control bounds and any non-zero probability of successful transmission over a noisy control channel.