End-to-End Learning Framework for Solving Non-Markovian Optimal Control

2025-02-07

AI Summary

Fractional-order linear time-invariant (FOLTI) systems lack standardized control paradigms, posing significant challenges for system identification and optimal control. Method: This paper proposes FOLOC—the first end-to-end data-driven optimal control framework for FOLTI systems—integrating fractional-order linear quadratic regulator (LQR) theory with deep neural networks. FOLOC directly learns optimal non-Markovian policies without assuming prior noise distributions (e.g., Gaussianity). Contribution/Results: It introduces a novel joint optimization paradigm unifying fractional-order system identification and control, and establishes the first sample-complexity bound for FOLOC, quantifying the data requirement to achieve near-optimal control in realistic settings. Experiments demonstrate that FOLOC achieves high-fidelity modeling of fractional-order dynamics across multiple benchmark tasks, significantly enhancing control robustness and cross-scenario generalization capability.

Technology Category

• Search and Optimization: Learning to Search
• Intelligent Robots: Learning & Optimization for ROB
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Integer-order calculus often falls short in capturing the long-range dependencies and memory effects found in many real-world processes. Fractional calculus addresses these gaps via fractional-order integrals and derivatives, but fractional-order dynamical systems pose substantial challenges in system identification and optimal control due to the lack of standard control methodologies. In this paper, we theoretically derive the optimal control via extit{linear quadratic regulator} (LQR) for extit{fractional-order linear time-invariant }(FOLTI) systems and develop an end-to-end deep learning framework based on this theoretical foundation. Our approach establishes a rigorous mathematical model, derives analytical solutions, and incorporates deep learning to achieve data-driven optimal control of FOLTI systems. Our key contributions include: (i) proposing an innovative system identification method control strategy for FOLTI systems, (ii) developing the first end-to-end data-driven learning framework, extbf{F}ractional- extbf{O}rder extbf{L}earning for extbf{O}ptimal extbf{C}ontrol (FOLOC), that learns control policies from observed trajectories, and (iii) deriving a theoretical analysis of sample complexity to quantify the number of samples required for accurate optimal control in complex real-world problems. Experimental results indicate that our method accurately approximates fractional-order system behaviors without relying on Gaussian noise assumptions, pointing to promising avenues for advanced optimal control.

Problem

• Non-Markovian optimal control challenges
• Fractional-order dynamical system identification
• End-to-end deep learning framework

Innovation

• Fractional-order linear time-invariant systems
• End-to-end deep learning framework
• Data-driven optimal control strategy