The Optimal Properties of Nonlinear Bilevel Multi-stage Dynamic System

For a kind of nonlinear multi-stage dynamic system and the properties its right function has, the existence and continuity with respect to the parameters of the solution have been discussed. We decompose the identification problem into bilevel multi-stage optimal control problem by the different parameter styles (time parameters and system parameters), and both of them are equivalence. Applying semi-infinite optimization and uniformly convex approximate, etc., we deduce the existence of optimal solution and necessary condition for optimality for the both original identification problem and bilevel multi-stage optimal control subproblems respectively. And it has been successfully applied to produce 1,3-propanediol in fermentation process (waiting for publication in another paper)