  Inverse optimal control (IOC) is about estimating an unknown objective of
interest given its optimal control sequence. However, truly optimal
demonstrations are often difficult to obtain, e.g., due to human errors or
inaccurate measurements. This paper presents an IOC framework for objective
estimation from multiple sub-optimal demonstrations in constrained
environments. It builds upon the Karush-Kuhn-Tucker optimality conditions, and
addresses the Errors-In-Variables problem that emerges from the use of
sub-optimal data. The approach presented is applied to various systems in
simulation, and consistency guarantees are provided for linear systems with
zero mean additive noise, polytopic constraints, and objectives with quadratic
features.
