Numerical Methods for Nonlinear Mixed-Integer Optimal Control Problems

This dissertation studies numerical methods for nonlinear mixed-integer optimal control problems governed by differential equations. The main focus is on problems in which continuous controls and discrete decisions have to be optimized together. Two application areas are considered. The first part develops a mixed-integer feedback control scheme based on direct multiple shooting and real-time iteration. A relaxed optimal control problem is solved first, and an admissible integer control is recovered using a maximum strategy motivated by Pontryagin’s Maximum Principle and switching functions. The second part treats optimum experimental design with sampling decisions as a mixed-integer optimal control problem. Binary sampling variables are used to describe when and which measurements are taken, so that experimental inputs and measurement schedules can be optimized jointly. The dissertation shows how relaxed continuous formulations, numerical optimal control methods, and optimality conditions can be combined to handle discrete decisions in dynamic optimization problems.