Computationally efficient stochastic MPC: a probabilistic scaling approach

Chance constrained sets approximation: A probabilistic scaling approach -- EXTENDED VERSION

“…The probabilistic scaling approach was presented in the conference papers [13,14]. The present work extends these in several directions: first, we performe here a thorough mathematical analysis the results, providing of all results.…”

“…Remark 2 (Sample-based SMPC) The learning theory-based approach discussed in this section has been applied in [11] to derive an offline probabilistic inner approximation of the chance constrained set X smpc ε defined in (14), considering individual chance constraints. In particular, the bound (2) is a direct extension to the case of joint chance constraints of the result proved in [11].…”

“…In particular, in case of 2 norm, the sets are ellipsoids. This particular choice is the one studied in [14]. Here, we extend this approach to a much more general family of sets, which encompasses for instance zonotopes, obtained by letting p = ∞ and s ≥ n θ .…”

Chance-constrained sets approximation: A probabilistic scaling approach

“…The probabilistic scaling approach was presented in the conference papers (Alamo, Mirasierra, Dabbene, & Lorenzen, 2019;Mammarella, Alamo, Dabbene, & Lorenzen, 2020) and it is based on recent results on order statistics (Alamo, Manzano, & Camacho, 2018). The present work extends Alamo et al (2019), Mammarella et al (2020) in several directions. First, we perform here a thorough mathematical analysis of probabilistic scaling.…”

“…In particular, in case of ℓ 2 norm, the sets are ellipsoids. This particular choice is the one studied in Mammarella et al (2020). Here, we extend this approach to a much more general family of sets, which encompasses for instance zonotopes, obtained by letting p = ∞ and s ≥ n θ .…”