Differential Dynamic Programming for Multistage Uncertain Optimal Control

When a multistage system is transferred from one stage to the next one, it could be affected by some disturbance. This kind of system is called a multistage uncertain system if the disturbance is an uncertain factor. Based on the uncertainty theory and the equation of optimality in uncertain optimal control, a differential dynamic programming algorithm for an optimal control problem subject to a multistage uncertain system is established. The differential dynamic programming algorithm is implemented from an initial nominal control, which is provided by the genetic algorithm, to an optimal control of the problem step by step. Finally, a numerical example that the system is nonlinear with the disturbance of linear uncertain variables is given to illustrate the feasibility of the algorithm.