The Combination of Adaptive Pseudospectral Method and Structure Detection Procedure for Solving Dynamic Optimization Problems with Discontinuous Control Profiles

To cope with computational challenges on dynamic optimization problems with discontinuous control profiles, a methodology combining the adaptive pseudospectral method with the structure detection procedure is presented. First, the adaptive pseudospectral method, which divides time intervals based on an estimation of approximation error, is utilized to obtain potential sequence and type of arcs composed of discontinuous control profiles. Second, the derived information is exploited by the structure detection procedure to reformulate the original nonsmooth problem as a multistage problem (MSP), where adjacent arcs with the same input type are merged into one to remove unnecessary LGR points for the final approximation. Additionally, a stop criterion by monitoring variations of the Hamiltonian function at discrete points is proposed to estimate whether the computed solution satisfies the necessary conditions of optimality in the sense of Pontryagin’s Minimum Principle. The efficiency of the proposed method i...

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