A recurrent neural network for hierarchical control of interconnected dynamic systems

Area of Science:

• Control Theory
• Artificial Intelligence
• Computational Neuroscience

Background:

• Interconnected dynamic systems present significant challenges for optimal control due to complexity and dimensionality.
• Existing numerical methods often suffer from high computational costs and slow convergence.
• Hierarchical control strategies offer a promising approach to manage complex systems.

Purpose of the Study:

• To develop a novel recurrent neural network for the optimal control of interconnected dynamic systems.
• To design a two-level hierarchical structure that decomposes and coordinates subsystems efficiently.
• To enhance computational efficiency and ensure stability in complex control scenarios.

Main Methods:

• A two-level hierarchical recurrent neural network architecture is proposed.
• A decomposition and coordination strategy is employed, utilizing a goal-coordination method.
• Dynamic equations are nested within local subnetworks to reduce dimensionality.
• The method is extended to handle bounded control inputs.

Main Results:

• The proposed neural network achieves a two-level hierarchical structure with concurrent processing at both levels.
• Significant reduction in neural network dimensionality is achieved by nesting dynamic equations.
• Computational efficiency is dramatically increased compared to traditional numerical algorithms.
• The neural network demonstrates asymptotic stability and satisfactory performance in an example case.

Conclusions:

• The developed recurrent neural network provides an efficient and stable solution for the optimal control of interconnected dynamic systems.
• The hierarchical structure and concurrent processing capabilities offer substantial computational advantages.
• The method's robustness is confirmed by its extension to bounded control inputs and stability analysis.