科研之友
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摘要
For the coupled PDE control problem, at time ti with the ith point, the standard algorithm will first obtain the two space variables (zi, vi) and then obtain the control variables (. opt i, mu opt i) from the given initial points (.0 i, mu 0 i). How many points i are determined by the facts of the case? We usually believe that the largest i defined by n is big because the small step size t = T- t0 n will generate a good approximation, where T denotes the terminal time. Thus, the solution process is very tedious, and much CPU time is required. In this paper, we present a new method to overcome this drawback. This presented method, which fully utilizes the first- order conditions, simultaneously considers the two space variables (zi, vi) and the control variables (. opt i, mu opt i) with ti at i. The computational complexity of the new algorithm is O(N3), whereas that of the normal algorithm is O(N3 + N3K). The performance of the proposed algorithm is tested using an example.
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