Functional Analysis, Calculus of Variations and Optimal Control

By F. Clarke. 2013

739 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/d25a9984bf4726abe4c570a68a4eec34e1fc638b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Francesco Rossi
2. Zhepei Wang
3. Fei Gao
4. Christian Clason
5. Chao Xu
6. F. Augeri
7. Xiaoxia Zhou
8. Benoît Bonnet

Citations in the corpus

• Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails (2015, background): “As a corollary of Danskin’s formula (see [11][Theorem 10.”
• The Pontryagin Maximum Principle in the Wasserstein Space (2017, background): “oblem studied here. Even though the derivation of a maximum principle under a merely Lipschitz-regularity assumption on the optimal control in the spirit of the non-smooth maximum principle (see e.g. [16]) might be available in this context, it would require a completely different approach and much m”
• A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems (2018, neutral): “s and subdifferential calculus in the space (P2(Rd),W2). We also introduce some elementary notions of non-smooth calculus in Banach spaces. For a complete introduction to these topics, see [9, 41] and [36, 19] respectively. 5 2.1 Analysis in measure spaces and the optimal transport problem In this Se”
• Robot Dance: A mathematical optimization platform for intervention against COVID-19 in a complex network (2022, background): “Furthermore, since (4) depends on the control linearly, when the function ψ is linear, the necessary optimality conditions given by Pontryagin maximum principle ensure that any optimal control is a concatenation of bang-bang and singular arcs [Cla13].”
• NONSMOOTH ANALYSIS AND OPTIMIZATION (2017, background): “Rather, like a magpie, I have collected the shiniest results and proofs I could nd, mainly from [Brokate 2014; Schirotzek 2007; Attouch, Buttazzo, et al. 2006; Bauschke & Combettes 2017; Clarke 2013; Ulbrich 2002; Schiela 2008].”
• Geometrically Constrained Trajectory Optimization for Multicopters (2021, methodology): “To analyze the optimality conditions for (20), we transform it from the Lagrangian form into Mayer form (Clarke 2013) by state augmentation.”