In this paper, we apply inverse optimal control approaches in order to recover the cost function that can explain given observations, for a class of constrained optimization problems. The inverse optimal control was recently solved in an approximately optimal framework, meaning that the interest is in finding the proper criteria suitable for the system for which the decisions are approximately optimal. This method benefits of computational time efficiency and simplicity while solving the inverse optimal control problem, by simplifying the initial optimization problem into least square ones, easier than the first one. We focused on solving problems where systems and observations are both imperfect and uncertain. First, we test this method when working with uncertain observations, and results show that the method is sensitive to model uncertainties, encountering bias problems. Being inspired by the approximately optimal approach, we, secondly, use the idea given by this approach and propose a bounded-error approach to inverse optimal control; where all uncertainty and disturbances acting on observation or modeling are assumed bounded but otherwise unknown. A set membership algorithm is then proposed that compute bounds on the set of criteria that make the uncertain observations optimal. Then we show that the bounds computed for the criterion contains the actual solution.
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