Formal Control for Uncertain Systems via Contract-Based Probabilistic Surrogates (Extended Version)

2025-06-20

AI Summary

Formal methods for high-dimensional uncertain stochastic systems suffer from poor scalability due to model complexity and struggle to simultaneously ensure correctness and performance guarantees. Method: This paper proposes a contract-based probabilistic surrogate modeling framework, the first to integrate contract theory with probabilistic simulation relations. It enables scalable abstraction-based control synthesis via controllably conservative design, circumventing explicit error-bound computation. Contribution/Results: The resulting surrogate model supports infinite-horizon probabilistic computational tree logic (PCTL*) verification. Evaluated on a high-dimensional autonomous intersection scenario, the approach achieves formal closed-loop control with a tenfold increase in state dimensionality while strictly satisfying both probabilistic correctness and real-time requirements.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Multiagent Systems under Uncertainty
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making with formal correctness and performance guarantees. Focusing on probabilistic simulation relations and surrogate models of stochastic systems, we propose an approach that significantly enhances the scalability and practical applicability of such simulation relations by eliminating the need to compute error bounds directly. As a result, we provide an abstraction-based technique that scales effectively to higher dimensions while addressing complex nonlinear agent-environment interactions with infinite-horizon temporal logic guarantees amidst uncertainty. Our approach trades scalability for conservatism favorably, as demonstrated on a complex high-dimensional vehicle intersection case study.

Problem

• Enhancing scalability of formal methods for uncertain systems
• Eliminating direct computation of error bounds in surrogate models
• Addressing nonlinear agent-environment interactions with temporal logic guarantees

Innovation

• Uses contract-based probabilistic surrogate models
• Eliminates direct error bounds computation
• Scales to high dimensions with temporal guarantees