Stochastic output feedback MPC with intermittent observations

Abstract

This paper considers constrained linear systems with stochastic additive disturbances and noisy measurements transmitted over a lossy communication channel. We propose a model predictive control (MPC) law that minimises a discounted cost subject to a discounted expectation constraint. Sensor data is assumed to be lost with known probability, and data losses are accounted for by expressing the predicted control policy as an affine function of future observations, which results in a convex optimal control problem. An online constraint-tightening technique ensures recursive feasibility of the online optimisation problem and satisfaction of the expectation constraint without imposing bounds on the distributions of the noise and disturbance inputs. The discounted cost evaluated along trajectories of the closed loop system is shown to be bounded by the initial optimal predicted cost. We also provide conditions under which the averaged undiscounted closed loop cost accumulated over an infinite horizon is bounded. Numerical simulations are described to illustrate these results.