Inverse optimal control for dynamic systems with inequality constraints

Inverse optimal control (IOC) algorithms can be used to reveal underlying objectives. Existing algorithms commonly estimate the objectives by assuming that the cost function can be represented as a weighted sum of features, and use optimality criteria to estimate the weights. However, the existing literature rarely discusses the recovery of cost functions in the presence of state or control constraints, which often exist due to the limited ranges of actuators and sensors. In this work, an optimisation problem is formulated to find the best values of weights and Lagrange multipliers of constraints to satisfy the optimality conditions, given a segment of an optimal trajectory. The maximum and minimum observed state and control variables are hypothesised as potential box constraints and validated by the associated Lagrange multipliers. In addition, this paper also introduces a method to dynamically choose the window size of the observation, or identify that not enough information was provided for an accurate estimation. The proposed approach is validated using simulated results generated with a two link serial arm. The results show the proposed approach can recover the cost function when box constraints are active, and the Lagrange multiplier value can indicate when and which constraints are present.