Optimal timing control of switched systems with applications to optimal bridge repairs

Abstract

Following results over recent years, this thesis enhances the problem of minimizing a cost functional defined on a state trajectory of an autonomous switched dynamical system. The cost functional traditionally used, is augmented with explicit costs on the switching times and the final time is set by a constraint as opposed to being given. An equation for the gradient of the cost functional is derived and an algorithm is proposed for computing local minima. The algorithm is based on existing steepest descent methods including the Armijo procedure and gradient projection. A matlab implementation of the algorithm is developed in order to solve optimal problems that can be modelled with costs on or between the switching times. An existing problem, the motivation for this research, where repairs on a bridge is to be optimized, is provided and solved.