Handling inverse optimal control problems using evolutionary bilevel optimization

Abstract

Optimal control is a task where it is desired to determine the inputs of a dynamical system that optimize (minimize or maximize) a specified cost functional, also known as performance index, while satisfying any constraints on behaviour of the system. As the name suggests, inverse optimal control is the opposite of the former one and thus is associated with mining of the cost functional, optimal behaviour of which fits the given results best. In this paper, we present the importance of evolutionary bilevel optimization techniques as a promising approach to solve inverse optimal control problems. Generally, inverse optimal control problems are found to be ill posed which makes them computationally expensive in addition to the associated redundancy with the solution. Inverse optimal control theory works as a stepping stone in figuring out the underlying optimality criteria in a given task. It has several other applications in areas like Markov's Decision Processes and Game Theory. In our work, we solve inverse optimal control problems to retrieve the original functional in optimal control task using metaheuristic based bilevel optimization techniques. The dataset comprising of state variables generated from an optimal control problem is utilized to mine the functional. In the later part of our paper, we formulate a problem of human motion transfer as a bilevel optimization task, and subsequently solve it using a bilevel algorithm.