Stochastic receding horizon control with output feedback and bounded controls

Authors:
Peter Hokayem;Eugenio Cinquemani;Debasish Chatterjee;Federico Ramponi;John Lygeros
Affiliations:
Automatic Control Laboratory, ETH Zürich, Physikstrasse 3, 8092 Zürich, Switzerland;INRIA Grenoble-Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, 38 334 Saint Ismier Cedex, France;Systems & Control Engineering, IIT Bombay, Powai, Mumbai 400076, India;Department of Information Engineering, Universití degli Studi di Brescia, via Branze 38, 25123 Brescia, Italy;Automatic Control Laboratory, ETH Zürich, Physikstrasse 3, 8092 Zürich, Switzerland
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

We study the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense. We then show how to augment the underlying optimization problem with a negative drift-like constraint, yielding a second-order cone program to be solved periodically online. We prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions. We also discuss how some quantities required by the finite-horizon optimization problem can be computed off-line, thus reducing the on-line computation.