Optimal switching instants for the control of hybrid systems

The problem of determining the optimal switching instants for the control of hybrid systems under reachability constraints is considered. This optimization problem is cast into an interval global optimization problem with differential constraints, where validated simulation techniques and a dynamic time meshing are used for the computation of its solution. The approach is applied on two examples, one being the well-known example of the Goddard’s problem where a rocket has to reach a given altitude while consuming the smallest amount of fuel, the second one considers a system with an higher dimension and a more complex optimization problem.