A Collage-Based Approach to Inverse Optimal Control Problems with Unique Solutions

Abstract

Optimal control problems entail finding a control function that optimizes a given objective functional, subject to a set of constraints that include an ordinary differential equation. Conversely, inverse optimal control problems entail seeking objective functionals that are optimized by a given control system. In this thesis we develop a Collage-Based Approach to solving inverse optimal control problems with unique solutions based on the Collage method for ODE inverse problems and Pontryagin’s Maximum Principle. Inverse problems are often formulated as the minimization of an approximation error over a set of parameters. Collage-type methods bound the approximation error by a quantity that is computationally preferable to optimize. We demonstrate this method through a variety of example scenarios and discuss its efficacy and robustness.