Multiperiod Optimization: Dynamic Programming vs. Optimal Control: Discussion

The title of this session pitting Dynamic Programming against Control Theory is misleading since dynamic programming (DP) is an integral part of the discipline of control theory. However, it is timely to discuss the relative merits of DP and other empirical solution approaches to control problems in agricultural economics, and equally importantly, how control theory can be used to pose more useful and realistic problems. From this point in the paper I shall, like Burt, use the term Dynamic Programming (DP) to mean the classic solution procedure developed by Bellman. All the other solution approaches used to solve multiperiod problems, including Differential Dynamic Programming [Jacobson and Mayne], are termed Control Theory. Burt takes the session title literally and rises to defend and extend the long history of DP research and application. I agree with him concerning the difficulty of teaching applied problem formulation, but like Zilberman, feel that lack of popularity of DP cannot be attributed to lack of exposure of graduate students. In his section on "Obstacles to Implementation" Burt is unjustifiably pessimistic in his judgement of the practicality and theoretical basis of solutions based on the Pontryagin Maximum principle. Given the long history of Pontryagin based control applications in engineering and operations research, the problems cannot be categorized in general as "trivial" or without "theorems on the structure of the solution." A comprehensive sur-