Safely Learning to Control the Linear Quadratic Regulator

Sarah Dean and Stephen Tu and Nikolai Matni and Benjamin Recht

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2019-41

May 15, 2019

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http://www2.eecs.berkeley.edu/Pubs/TechRpts/2019/Archive/EECS-2019-41.pdf

We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of state and input constraints. This framework involves a novel method for synthesizing robust constraint-satisfying feedback controllers, leveraging newly developed tools from system level synthesis. We connect statistical results with cost sub-optimality bounds to give non-asymptotic guarantees on both estimation and controller performance.

Advisors: Benjamin Recht

BibTeX citation:

@mastersthesis{Dean:EECS-2019-41,
    Author= {Dean, Sarah and Tu, Stephen and Matni, Nikolai and Recht, Benjamin},
    Title= {Safely Learning to Control the Linear Quadratic Regulator},
    School= {EECS Department, University of California, Berkeley},
    Year= {2019},
    Month= {May},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2019/EECS-2019-41.html},
    Number= {UCB/EECS-2019-41},
    Abstract= {We study the constrained linear quadratic regulator with unknown dynamics,
addressing the tension between safety and exploration in data-driven control techniques.
We present a framework which allows for system identification through persistent excitation,
while maintaining safety by guaranteeing the satisfaction of state and input constraints.
This framework involves a novel method for synthesizing robust constraint-satisfying feedback controllers, leveraging newly developed tools from 
system level synthesis.
We connect statistical results with cost sub-optimality bounds to give
non-asymptotic guarantees on both estimation and controller performance.},
}

EndNote citation:

%0 Thesis
%A Dean, Sarah 
%A Tu, Stephen 
%A Matni, Nikolai 
%A Recht, Benjamin 
%T Safely Learning to Control the Linear Quadratic Regulator
%I EECS Department, University of California, Berkeley
%D 2019
%8 May 15
%@ UCB/EECS-2019-41
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2019/EECS-2019-41.html
%F Dean:EECS-2019-41