Scalable and Approximation-free Symbolic Control for Unknown Euler-Lagrange Systems

2025-09-24

AI Summary

This paper addresses trajectory control of uncertain Euler–Lagrange systems with bounded but unknown parameters, requiring strict satisfaction of continuous-time temporal logic specifications. Method: We propose a model-free, scalable, and approximation-free symbolic control framework that integrates virtual-system abstraction based on parameter bound estimation, closed-form model-free controller synthesis, and confinement-region construction. The approach explicitly handles input constraints and exogenous disturbances without relying on exact dynamical models. Contribution/Results: To the best of our knowledge, this is the first method ensuring full-trajectory correctness guarantees for such systems without precise dynamics knowledge. It significantly reduces computational complexity compared to conventional symbolic control approaches—whether model-based or discretization-dependent—enabling real-time deployment. Experimental validation on a pendulum, a two-link robotic manipulator, and a multi-agent system demonstrates safety, robustness against parametric uncertainty and disturbances, and hardware feasibility.

Technology Category

• Multiagent Systems: Multiagent Systems under Uncertainty
• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We propose a novel symbolic control framework for enforcing temporal logic specifications in Euler-Lagrange systems that addresses the key limitations of traditional abstraction-based approaches. Unlike existing methods that require exact system models and provide guarantees only at discrete sampling instants, our approach relies only on bounds on system parameters and input constraints, and ensures correctness for the full continuous-time trajectory. The framework combines scalable abstraction of a simplified virtual system with a closed-form, model-free controller that guarantees trajectories satisfy the original specification while respecting input bounds and remaining robust to unknown but bounded disturbances. We provide feasibility conditions for the construction of confinement regions and analyze the trade-off between efficiency and conservatism. Case studies on pendulum dynamics, a two-link manipulator, and multi-agent systems, including hardware experiments, demonstrate that the proposed approach ensures both correctness and safety while significantly reducing computational time and memory requirements. These results highlight its scalability and practicality for real-world robotic systems where precise models are unavailable and continuous-time guarantees are essential.

Problem

• Enforcing temporal logic specifications for unknown Euler-Lagrange systems
• Ensuring continuous-time correctness without exact system models
• Providing robust control under input constraints and disturbances

Innovation

• Model-free controller using system parameter bounds
• Scalable abstraction of simplified virtual system
• Continuous-time correctness with input constraint guarantees