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Control over erasure channels: stochastic stability and performance of packetized unconstrained model predictive control


Correspondence to: Marcus Reble, Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany.



In this work, we consider the control of discrete-time constrained nonlinear systems over unreliable packet-based communication networks. The random packet dropouts are modeled by a two-state Markov chain, and no acknowledgments of receipt are assumed. To weaken the impact of the packet dropouts, the controller transmits packets containing more than one future control input, and a suitable buffering is applied at the plant actuator side. Because the Markov chain model adopted does not ensure the number of consecutive packet dropouts to be bounded, deterministic stability cannot be guaranteed. Hence, we are interested in stochastic stability of the closed loop instead. We propose an unconstrained model predictive control scheme without additional terminal weighting term for the calculation of the control inputs. Two major advantages of this unconstrained model predictive control scheme can be emphasized. First, to guarantee stochastic stability, we do not require the knowledge of a global control Lyapunov function as terminal cost term but instead only a less restrictive controllability assumption. Second, guaranteed performance bounds on the expected infinite horizon cost of the closed loop can be obtained. Copyright © 2012 John Wiley & Sons, Ltd.