Stochastic output feedback MPC with intermittent observations

TL;DR

This paper develops a stochastic output feedback MPC for linear systems with intermittent observations, ensuring constraint satisfaction and cost bounds despite data losses modeled by a Bernoulli process.

Contribution

It introduces a convex linear-quadratic control formulation for systems with stochastic sensor data losses, providing robustness analysis and cost guarantees.

Findings

Constraint satisfaction is maintained despite data losses.

The control law ensures a finite long-term average cost.

Robustness bounds quantify the impact of observation probability uncertainties.

Abstract

This paper designs a model predictive control (MPC) law for constrained linear systems with stochastic additive disturbances and noisy measurements, minimising a discounted cost subject to a discounted expectation constraint. It is assumed that sensor data is lost with a known probability. Taking into account the data losses modelled by a Bernoulli process, we parameterise the predicted control policy as an affine function of future observations and obtain a convex linear-quadratic optimal control problem. Constraint satisfaction and a discounted cost bound are ensured without imposing bounds on the distributions of the disturbance and noise inputs. In addition, the average long-run undiscounted closed loop cost is shown to be finite if the discount factor takes appropriate values. We analyse robustness of the proposed control law with respect to possible uncertainties in the arrival probability of sensor data and we bound the impact of these uncertainties on constraint satisfaction and the discounted cost. Numerical simulations are provided to illustrate these results.