Differential Dynamic Programming For Multistage Uncertain Optimal Control

Multistage optimal control problem is an important topic in the field of the con-trol. When a system is transferred from one stage to next one, it could be affected by some disturbance, which is not usually considered as stochastic or fuzzy, but uncertain. This kind of system is called the multistage uncertain system.Based on the uncertainty theory established by Professor Liu Baoding and the equation of optimality in uncertain optimal control proposed by Professor Zhu Yuan-guo, a differential dynamic programming algorithm for the multistage system uncertain optimal control is obtained. Applying the hybrid genetic algorithm, a kind of intelli-gent optimization algorithms, which are good at global searching, an optimal nominal control for the differential dynamic programming algorithm could be got. Finally, to illustrate the feasibility and convergence of the algorithm, two numerical examples that the systems and objective functions are nonlinear with the disturbance variables subject to linear and normal respectively are given in the last part of the article.