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

Area of Science:

• Control Engineering
• Artificial Intelligence
• Computational Modeling

Background:

• Classical optimal control problems often rely on explicit dynamic models, which are not always available.
• Simulation models, like hybrid models using functional mockup units, generate input-output data but lack explicit state equations.
• Treating these complex systems as black-box models is necessary when internal dynamics are unknown.

Purpose of the Study:

• To develop a method for creating accurate surrogate models for the right-hand-side derivative functions of state equations in black-box systems.
• To improve the solution of optimal control problems when only input-output data is available.
• To validate the proposed method's effectiveness on both mathematical and real-world engineering problems.

Main Methods:

• Utilized hierarchical neural networks to surrogate the unknown derivative functions of state equations.
• Developed a spatial adaptive partitioning criterion that integrates global sensitivity indices and local space interval lengths.
• Trained and compared surrogate models using the proposed partitioning criterion against other methods based on input-output data.

Main Results:

• The spatial adaptive partitioning method yielded surrogate models with higher accuracy compared to other partitioning criteria.
• Numerical results demonstrated the superior performance of the proposed method in approximating the black-box model dynamics.
• The strategy proved effective in a trajectory optimization problem involving a black-box industrial robot (Manutec r3).

Conclusions:

• The proposed spatial adaptive partitioning strategy effectively generates accurate hierarchical neural network surrogate models for black-box systems.
• This approach offers a viable solution for optimal control problems lacking explicit dynamic models.
• The method's practical applicability is confirmed through successful application to a complex industrial robot system.