Bellman R. Introduction to the Mathematical Theory of Control Processes. Volume 2. Nonlinear Processes

Academic Press, 1971. — 327 p.The order of presentation is the reverse of the order in Volume I where the calculus of variations was treated first. There the motivation was that a
simple rigorous account could easily be given and that this approach could in turn be used to provide a rigorous derivation of the fundamental Riccati
equation of dynamic programming. Here we use dynamic programming to provide a simple rigorous approach to general discrete control processes. At the cost of essentially no additional effort, we can in this way handle constraints and stochastic effects. On the other hand, the consideration of these important aspects of general continuous processes requires a non-negligible mathematical training and sophistication.