Strong unimodality

Bertin, Emile M. J.; Cuculescu, Ioan; Theodorescu, Radu

doi:10.1007/978-94-015-8808-9_6

Cited by 5 publications

(3 citation statements)

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“…Hence, the pdf is log concave when N s ≥ 4. Since log concave distributions are also unimodal [16], we can conclude that ( 19) is unimodal when N s ≥ 4.…”

Section: B Polytopic Target Set Constraintmentioning

confidence: 80%

“…, and probabilistic violation threshold α < 1/6. Definition 1 (Unimodal Distribution [11]). A unimodal distribution is a distribution whose cumulative distribution function is convex in the region (−∞, a) and concave in the region (a, ∞) for some a ∈ R. Assumption 1.…”

Section: A Problem Formulationmentioning

confidence: 99%

“…Definition 2 (Strong Unimodal Distribution [11]). A strong unimodal distribution is one in which unimodality is preserved by convolution.…”

Section: A Problem Formulationmentioning

confidence: 99%

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Approximate Quantiles for Stochastic Optimal Control of LTI Systems with Arbitrary Disturbances

Priore¹,

Petersen²,

Oishi³

2022

2022 American Control Conference (ACC)

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We propose an open loop control scheme for linear time invariant systems perturbed by multivariate 𝑡 disturbances through the use of quantile reformulations. The multivariate 𝑡 disturbance is motivated by heavy tailed phenomena that arise in multi-vehicle planning planning problems through unmodeled perturbation forces, linearization effects, or faulty actuators. Our approach relies on convex quantile reformulations of the polytopic target sets * Graduate student, Department of Electrical and Computer Engineering † Professor, Department of Electrical and Computer Engineering

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“…Hence, the pdf is log concave when N s ≥ 4. Since log concave distributions are also unimodal [16], we can conclude that ( 19) is unimodal when N s ≥ 4.…”

Section: B Polytopic Target Set Constraintmentioning

confidence: 80%

Section: A Problem Formulationmentioning

confidence: 99%