Optimal control of discrete systems: Recent results and case studies

The paper has two main purposes: to give an introduction to some fundamental results of discrete-time optimal control and to show that they are useful to solve various types of problems. Maximum principles, which represent fundamental optimization principles within optimal control theory, such as the weak, the strong, the generalized and the global maximum principles are presented. Four case studies will illustrate the application of these maximum principles: an assortment problem, the optimal design of a wall, a pump-pipe system design and a consumer brand choice model.