Augmented Physics-Based Models for High-Order Markov Filtering

Area of Science:

• Control Theory
• Machine Learning
• Dynamical Systems

Background:

• Augmented physics-based models (APBMs) integrate physical laws with data-driven approaches for interpretable modeling.
• High-order Markov models require state augmentation for accurate state estimation, often necessitating complete knowledge of system dynamics.

Purpose of the Study:

• Extend APBMs to high-order Markov models using state augmentation (AG-APBM).
• Develop an approximated-state APBM (AP-APBM) to reduce computational burden.
• Evaluate AG-APBM and AP-APBM performance against standard APBMs.

Main Methods:

• Augmenting the state space with past states for high-order Markov models (AG-APBM).
• Implementing an approximated-state APBM (AP-APBM) using past time step summaries.
• Testing models on autoregressive and target-tracking scenarios with delayed feedback control.

Main Results:

• Both AG-APBM and AP-APBM outperformed standard APBMs in reducing estimation error.
• AG-APBM reduced autoregressive model estimation error by 31.1%; AP-APBM reduced it by 26.7%.
• AP-APBM achieved significant reductions in time cost (37.5%) and memory usage (20%) compared to AG-APBM.

Conclusions:

• The proposed AG-APBM and AP-APBM effectively handle high-order Markov models without requiring full dynamic knowledge.
• AP-APBM offers a computationally efficient alternative to AG-APBM with minimal performance degradation.
• These methods enhance state estimation accuracy and efficiency in complex control systems.