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Stochastic receding horizon control with output feedback and bounded controls

Peter Hokayem 1 Eugenio Cinquemani 2, * Debasish Chatterjee 1 Federico Ramponi 1 John Lygeros 1
* Corresponding author
2 IBIS - Modeling, simulation, measurement, and control of bacterial regulatory networks
LAPM - Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble], Inria Grenoble - Rhône-Alpes, Institut Jean Roget
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.
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Peter Hokayem, Eugenio Cinquemani, Debasish Chatterjee, Federico Ramponi, John Lygeros. Stochastic receding horizon control with output feedback and bounded controls. Automatica, Elsevier, 2012, 48 (1), pp.77-88. ⟨10.1016/j.automatica.2011.09.048⟩. ⟨hal-00762600⟩

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