Learning Robust Predictive Control: A Spatial-Temporal Game Theoretic Approach.

Area of Science:

• Control Theory
• Machine Learning
• Dynamical Systems

Background:

• Model-driven control methods are limited by unavailable system dynamics.
• Robust predictive control is crucial for uncertain environments.
• Time consistency is a key factor in control system stability.

Purpose of the Study:

• To develop a learning robust predictive control (LRPC) framework for unknown dynamical systems.
• To reconstruct the control problem as spatial-temporal games.
• To guarantee system stability using time-consistent Nash equilibrium.

Main Methods:

• Utilizing multistep feedback-like control causality derived from time series analysis and Takens' theorem.
• Reconstructing the control problem as spatial-temporal games (temporal nonzero-sum and spatial zero-sum subgames).
• Employing multistep reinforcement learning (RL) with neural network function approximation for model-free control and stability analysis.

Main Results:

• The proposed LRPC framework effectively solves robust predictive control problems for unknown systems.
• Stability is guaranteed through the derivation of time-consistent Nash equilibrium.
• Convergence of the RL approach is proven via oscillatory value function bounds analysis.

Conclusions:

• The developed LRPC framework offers a robust and effective solution for controlling unknown dynamical systems.
• The spatial-temporal game reconstruction and RL-based approach provide a novel method for achieving stable control.
• Data-driven implementation using neural networks demonstrates the practical applicability and effectiveness of the proposed method.