Output feedback model predictive control with probabilistic uncertainties for linear systems

Abstract

In many control problems, not all states can be measured and the system is subject to parametric uncertainties, measurement noise, and hard input constraints. To tackle such problems for linear systems, we propose to combine a recursive parameter and state estimator based on Bayes' theorem with a stochastic model predictive control approach. To efficiently obtain the probability density functions for the random variables and to propagate the uncertainties, Polynomial chaos theory is used. The parameter and state distributions are recursively estimated via Bayes' theorem, which is solved as a nonlinear least-squares problem. These distributions are utilized in a polynomial chaos based robust model predictive controller to steer the system to the desired reference while satisfying input constraints. The efficiency and properties of the resulting output feedback strategy are illustrated with two example systems, a simple paper-machine example, and the control of a chemical process.