PhD Position on Data-Driven Distributional Inference for Reliable Control of Complex Systems

Updated: 27 days ago
Deadline: 16 Jun 2021

Decisions under uncertainty are ubiquitous in control engineering and seek to provide quantitative solutions when complexity or lack of knowledge about the underlying systems require the probabilistic modeling of their components. Such random elements are often dynamic and the designer needs to make inferences about them using a limited amount of data. Furthermore, the data may only reveal partial-state information about the process, which is often corrupted by noise. All these factors hinder the possibility of making accurate inferences about the underlying probabilistic models and their usage for control design. 

To address these issues, this PhD project will leverage tools from state estimation and uncertainty quantification to fuse information from both the data and the known system dynamics and provide robust uncertainty descriptions for reliable decisions and control. The goal is to obtain plausible models about the evolving uncertainty from small data sets based on first-principles assumptions like the classes where the unknown distributions of random initial conditions, parameters, and noise elements belong [1, 2]. Specifically, one seeks to build ambiguity sets of probability distributions that contain the evolving true distribution of the data with high probability and exploit them to take reliable control actions. 

The approach will combine techniques across control engineering and applied mathematics, including tools from filtering and nonlinear state estimation, optimization, uncertainty quantification, optimal transport, and high-dimensional probability [3, 4]. The developed data-driven inference and control algorithms will be applied to domains like robotics, power systems, and transportation.

Related work and literature:

[1] D. Boskos, J. Cortés, and S. Martínez, Data-driven ambiguity sets with probabilistic guarantees for dynamic processes, IEEE Transactions on Automatic Control, 66(7), 2021, to appear, (arXiv:1909.11194).

[2] D. Boskos, J. Cortés, and S. Martínez, High-confidence data-driven ambiguity sets for time-varying linear systems, 2021, (arXiv:2102.01142).

[3] F. Santambrogio, Optimal transport for applied mathematicians, Birkäuser, NY, 2015.

[4] R. Vershynin, High-dimensional probability: An introduction with applications in data science, Cambridge university press, 2018.

The department Delft Center for Systems and Control (DCSC) of the faculty Mechanical, Maritime and Materials Engineering, coordinates the education and research activities in systems and control at Delft University of Technology. The Centers' research mission is to conduct fundamental research in systems dynamics and control, involving dynamic modelling, advanced control theory, optimisation and signal analysis. The research is motivated by advanced technology development in physical imaging systems, renewable energy, robotics and transportation systems.

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