Optimal control of a black-box system based on surrogate models by spatial adaptive partitioning method

When the dynamic model of a classical optimal control problem is explicit, we can transform this problem into a nonlinear programming problem and solve it by employing a traditional method. However, in some cases, no mathematical model of state equations is provided explicitly except for input-output data obtained from a simulation model. The hybrid model composed of functional mockup unit blocks generated in multiple platforms is a typical example. In this work, we regard these blocks as black-box models and use hierarchical neural network model to surrogate right-hand-side derivative functions of state equations. Specifically, to obtain highly accurate hierarchical neural network model, we explore a spatial adaptive partitioning criterion combining global sensitivity indices and interval length of local spaces based on the input-output data. Compared with models trained by several other partition criteria, numerical results verify that surrogate models obtained by the spatial adaptive partitioning method have higher accuracy. A mathematical example and a trajectory optimization problem of the black-box industrial robot Manutec r3 indicate the effectiveness of our proposed strategy.