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Robust and stochastic MPC of uncertain-parameter systems

Robust and stochastic MPC of uncertain-parameter systems
Robust and stochastic MPC of uncertain-parameter systems
Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with a choice of using conservative bounds that may give poor performance, or accurate ones that require heavy online computation. This thesis presents a framework to achieve a more flexible trade-off between these two extremes by using a state tube, a sequence of parametrised polyhedra that is guaranteed to contain the future state.

To define controllers using a tube, one must ensure that the polyhedra are a sub-set of the region defined by constraints. Necessary and sufficient conditions for these subset relations follow from duality theory, and it is possible to apply these conditions to constrain predicted system states and inputs with only a little conservatism. This leads to a general method of MPC design for uncertain-parameter systems. The resulting controllers have strong theoretical properties, can be implemented using standard algorithms and outperform existing techniques.

Crucially, the online optimisation used in the controller is a convex problem with a number of constraints and variables that increases only linearly with the length of the prediction horizon. This holds true for both LDI and LPV systems. For the latter it is possible to optimise over a class of gain-scheduled control policies to improve performance, with a similar linear increase in problem size.

The framework extends to stochastic LDIs with chance constraints, for which there are efficient suboptimal methods using online sampling. Sample approximations of chance constraint-admissible sets are generally not positively invariant, which motivates the novel concept of ‘sample-admissible’ sets with this property to ensure recursive feasibility when using sampling methods. The thesis concludes by introducing a simple, convex alternative to chance-constrained MPC that applies a robust bound to the time average of constraint violations in closed-loop.
University of Oxford
Fleming, James
b59cb762-da45-43b1-b930-13dd9f26e148
Fleming, James
b59cb762-da45-43b1-b930-13dd9f26e148
Cannon, Mark
d2a52d25-9100-4a93-9bc7-8d10f4f3fa17
Kouvaritakis, Basil
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Fleming, James (2016) Robust and stochastic MPC of uncertain-parameter systems. University of Oxford, Doctoral Thesis, 213pp.

Record type: Thesis (Doctoral)

Abstract

Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with a choice of using conservative bounds that may give poor performance, or accurate ones that require heavy online computation. This thesis presents a framework to achieve a more flexible trade-off between these two extremes by using a state tube, a sequence of parametrised polyhedra that is guaranteed to contain the future state.

To define controllers using a tube, one must ensure that the polyhedra are a sub-set of the region defined by constraints. Necessary and sufficient conditions for these subset relations follow from duality theory, and it is possible to apply these conditions to constrain predicted system states and inputs with only a little conservatism. This leads to a general method of MPC design for uncertain-parameter systems. The resulting controllers have strong theoretical properties, can be implemented using standard algorithms and outperform existing techniques.

Crucially, the online optimisation used in the controller is a convex problem with a number of constraints and variables that increases only linearly with the length of the prediction horizon. This holds true for both LDI and LPV systems. For the latter it is possible to optimise over a class of gain-scheduled control policies to improve performance, with a similar linear increase in problem size.

The framework extends to stochastic LDIs with chance constraints, for which there are efficient suboptimal methods using online sampling. Sample approximations of chance constraint-admissible sets are generally not positively invariant, which motivates the novel concept of ‘sample-admissible’ sets with this property to ensure recursive feasibility when using sampling methods. The thesis concludes by introducing a simple, convex alternative to chance-constrained MPC that applies a robust bound to the time average of constraint violations in closed-loop.

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More information

Published date: October 2016

Identifiers

Local EPrints ID: 422578
URI: http://eprints.soton.ac.uk/id/eprint/422578
PURE UUID: 5e2d852f-2745-4f8e-b2ef-1c4a1aecbb79
ORCID for James Fleming: ORCID iD orcid.org/0000-0003-2936-4644

Catalogue record

Date deposited: 25 Jul 2018 16:30
Last modified: 05 Jun 2024 17:16

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Contributors

Author: James Fleming ORCID iD
Thesis advisor: Mark Cannon
Thesis advisor: Basil Kouvaritakis

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