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Stochastic MPC for additive and multiplicative uncertainty using sample approximations

Stochastic MPC for additive and multiplicative uncertainty using sample approximations
Stochastic MPC for additive and multiplicative uncertainty using sample approximations
We introduce an approach for Model Predictive Control (MPC) of systems with additive and multiplicative stochastic uncertainty subject to chance constraints. Predicted states are bounded within a tube and the chance constraint is considered in a ‘one step ahead’ manner, with robust constraints applied over the remainder of the horizon. The online optimization is formulated as a chance-constrained program which is solved approximately using sampling. We prove that if the optimization is initially feasible, it remains feasible and the closed-loop system is stable. Applying the chance-constraint only one step ahead allows us to state a confidence bound for satisfaction of the chance constraint in closed-loop. Finally, we demonstrate by example that the resulting controller is only mildly more conservative than scenario MPC approaches that have no feasibility guarantee.
MPC, stochastic control, Predictive Control, Sampling, Robust control
0018-9286
Fleming, James
b59cb762-da45-43b1-b930-13dd9f26e148
Cannon, Mark
d2a52d25-9100-4a93-9bc7-8d10f4f3fa17
Fleming, James
b59cb762-da45-43b1-b930-13dd9f26e148
Cannon, Mark
d2a52d25-9100-4a93-9bc7-8d10f4f3fa17

Fleming, James and Cannon, Mark (2018) Stochastic MPC for additive and multiplicative uncertainty using sample approximations. IEEE Transactions on Automatic Control. (doi:10.1109/TAC.2018.2887054).

Record type: Article

Abstract

We introduce an approach for Model Predictive Control (MPC) of systems with additive and multiplicative stochastic uncertainty subject to chance constraints. Predicted states are bounded within a tube and the chance constraint is considered in a ‘one step ahead’ manner, with robust constraints applied over the remainder of the horizon. The online optimization is formulated as a chance-constrained program which is solved approximately using sampling. We prove that if the optimization is initially feasible, it remains feasible and the closed-loop system is stable. Applying the chance-constraint only one step ahead allows us to state a confidence bound for satisfaction of the chance constraint in closed-loop. Finally, we demonstrate by example that the resulting controller is only mildly more conservative than scenario MPC approaches that have no feasibility guarantee.

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Accepted/In Press date: 2 December 2018
e-pub ahead of print date: 17 December 2018
Keywords: MPC, stochastic control, Predictive Control, Sampling, Robust control

Identifiers

Local EPrints ID: 426829
URI: http://eprints.soton.ac.uk/id/eprint/426829
ISSN: 0018-9286
PURE UUID: 21f243e7-5518-4c94-847c-4641ae192b2e
ORCID for James Fleming: ORCID iD orcid.org/0000-0003-2936-4644

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Date deposited: 13 Dec 2018 12:19
Last modified: 20 Jul 2019 04:04

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Contributors

Author: James Fleming ORCID iD
Author: Mark Cannon

University divisions

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