Journal
AUTOMATICA
Volume 60, Issue -, Pages 182-188Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2015.07.013
Keywords
Scenario optimization; Random convex programs; Chance constraints; Randomized Model Predictive Control; Stochastic Model Predictive Control
Funding
- Swiss Nano-Tera.ch under the project HeatReserves
- European Commission [FP7-ICT 619435]
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The scenario approach provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (scenarios). The sample size critically depends on Helly's dimension, a-quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly's dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback. (C) 2015 Elsevier Ltd. All rights reserved.
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