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

Abstract

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.