Impulse control: Boolean programming and numerical algorithms

A numerical algorithmic approach to the impulse control problem is considered. Impulse controls are modelled by Boolean binary variables. The impulse Gateaux derivatives for impulse times, impulse volumes and Boolean variables are derived, and these are applied to the numerical algorithms. These algorithms require significantly less computation time and memory storage than the quasi-variational inequalities by Bensoussan-Lions. By using our algorithms, complicated models of hybrid or constrained systems can be more easily treated numerically than by using Pontryagin´s Minimum Principle. Numerical experiments are performed for models on capacity expansion in a manufacturing plant, and on impulse control of Verhulst systems and Lotka-Volterra systems; the results confirm the effectiveness of the proposed method