  We propose a control design method for linear time-invariant systems that
iteratively learns to satisfy unknown polyhedral state constraints. At each
iteration of a repetitive task, the method constructs an estimate of the
unknown environment constraints using collected closed-loop trajectory data.
This estimated constraint set is improved iteratively upon collection of
additional data. An MPC controller is then designed to robustly satisfy the
estimated constraint set. This paper presents the details of the proposed
approach, and provides robust and probabilistic guarantees of constraint
satisfaction as a function of the number of executed task iterations. We
demonstrate the safety of the proposed framework and explore the safety vs.
performance trade-off in a detailed numerical example.
