  A key challenge in solving the deterministic inverse reinforcement learning
(IRL) problem online and in real-time is the existence of multiple solutions.
Nonuniqueness necessitates the study of the notion of equivalent solutions,
i.e., solutions that result in a different cost functional but same feedback
matrix, and convergence to such solutions. While offline algorithms that result
in convergence to equivalent solutions have been developed in the literature,
online, real-time techniques that address nonuniqueness are not available. In
this paper, a regularized history stack observer that converges to
approximately equivalent solutions of the IRL problem is developed. Novel
data-richness conditions are developed to facilitate the analysis and
simulation results are provided to demonstrate the effectiveness of the
developed technique.
