Sparse Control of Linear Dynamical Systems with Application to Wind Farm Control

Sparse control refers to the use of a few actuation channels to enforce a desired behavior in a controlled dynamical system, even when a much larger availability of actuation is present. As counterintuitive as it may initially seem, exploiting sparsity in control is indeed an attractive trend for various reasons. For example, in networked control systems, control inputs may be transmitted over wireless channels, and sparse signals allow for compressed representations that can be sent faster, more reliably, and using fewer communication resources. In the control of opinions over social networks, such as spreading relevant news, it may be sufficient to leverage a few influential users who, in turn, will influence most of the social network. In wind farm control, where wind turbines can be partially reconfigured to fairly "share" incoming wind and maximize overall energy production, a handful of strategic turbines may be selected to reduce the wearing of blades due to load fatigue and thus increase the lifespan of all turbines.

Interestingly enough, while systems theory covers nearly all that can be possibly understood about the control of linear systems, embedding sparsity constraints in the controls is a relatively young research area. Early works, motivated by feedback control of networked and large-scale systems, have been dealing with the optimal design of sparse feedback gains. Here, feedback gains are typically associated with communication links between different subsystems (e.g., two wind turbines), implying that a sparse controller uses a few links. Recent work has taken a different route, imposing sparsity directly in the control inputs and studying controllability properties by mixing classical systems theory with the compressed sensing literature. However, the effective design of sparse control input signals to impose a desired state trajectory remains largely unexplored.

Assignment

This thesis targets two contributions. The first is to explore algorithms for the (optimal) design of control inputs subject to sparsity constraints. The second is to apply the developed sparse control algorithms to the control of a wind farm, with a focus on the reduction of load fatigue and wearing of blades compared to state-of-the-art wind farm control strategies. The thesis is jointly supervised by Geethu Joseph and Luca Ballotta in close collaboration with DCSC, ME.

Requirements

For this project, we are looking for a master's student in either electrical engineering or any related study. Furthermore, we are looking for a student who has a background in signal processing/control theory, basic statistical techniques, and programming skills in Matlab, Python, and/or C/C++. Strong communication (written and verbal) skills in English are mandatory. 

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Last modified: 2024-03-11