Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systems.

Area of Science:

• Robotics
• Artificial Intelligence
• Control Theory

Background:

• Neural networks are widely used in robotics for various functions.
• Analyzing learned behaviors in neural networks is crucial for understanding system performance.
• Existing methods for computing control invariant sets and regions of attraction are limited.

Purpose of the Study:

• To develop methods for computing control invariant sets and regions of attraction (ROAs) for dynamical systems represented by neural networks.
• To analyze learned behaviors in neural networks used in robotics.
• To improve the understanding of closed-loop performance in robotic systems.

Main Methods:

• Focus on feedforward neural networks with Rectified Linear Unit (ReLU) activation, which implement continuous piecewise-affine (PWA) functions.
• Developed the Reachable Polyhedral Marching (RPM) algorithm to enumerate affine pieces of a neural network.
• Used RPM to compute exact forward and backward reachable sets for control invariant sets and ROAs.
• Proposed an accelerated algorithm for computing ROAs, achieving a 15x speedup.

Main Results:

• Successfully computed control invariant sets and ROAs for learned van der Pol oscillator and pendulum models.
• Demonstrated the ability to find nonconvex control invariant sets and ROAs.
• Applied the methods to stabilize states for an image-based controller in an aircraft runway control problem.
• The accelerated ROA computation showed significant speedup.

Conclusions:

• The developed methods provide a novel, incremental approach to compute control invariant sets and ROAs for neural network models.
• This work enables better analysis of learned behaviors and closed-loop performance in robotics.
• The approach is effective for complex systems and offers computational advantages.