Discrepancy Computation for Nonlinear System Verification
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Solution Overview
Problem
Current simulation-based verification algorithms for nonlinear and hybrid systems are limited in providing formal safety guarantees, especially for models with large sets of initial conditions, inputs, and unknown parameters, as they rely on user-provided discrepancy functions and are not effective for large systems.
Innovation Solution
The development of an algorithm that computes piecewise exponential discrepancy functions for control systems interacting with physical processes, eliminating the need for user-provided annotations by using local convergence or divergence rates of trajectories and bounding the maximal eigenvalue of the Jacobian, allowing for compositional analysis and verification of safety without requiring all subsystem discrepancies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If simulation-based verification algorithms are used for nonlinear and hybrid systems, then confidence for design and testing is improved, but formal safety guarantees are insufficient
Solution Approach 1:
The patent introduces reachtubes as an intermediary mathematical construct that bridges simulation-based verification and formal safety guarantees. Reachtubes provide over-approximations of reachable states, enabling formal verification of safety properties while maintaining compatibility with simulation approaches for nonlinear and hybrid systems.
Solution Approach 2:
The patent performs preliminary computation of discrepancy functions and reachtubes before formal verification. By pre-computing these mathematical constructs that capture system behavior over time intervals, the algorithm establishes formal safety guarantees in advance rather than requiring exhaustive exploration during verification.
2Productivity
If user-provided discrepancy functions are used, then verification can be performed, but the method is not effective for large systems with many initial conditions and parameters
Solution Approach 1:
The patent implements self-service by automatically computing discrepancy functions from the system model itself, eliminating the need for manual user provision. The algorithm derives discrepancy functions by analyzing the system's own dynamics and Jacobian matrices, enabling scalable verification of large systems without requiring extensive user annotation effort.
Solution Approach 2:
The patent transforms the verification approach by changing from fixed user-provided discrepancy functions to dynamically computed ones based on system parameters. By computing discrepancy functions that adapt to the specific system being verified, the method efficiently handles large systems with varying initial conditions and parameters.
3Reliability
If reachtubes are computed from simulations, then over-approximations of all possible behaviors are obtained, but the computation requires user-provided annotations
Solution Approach 1:
The patent enables reachtube computation to be self-sufficient by automatically generating discrepancy functions from the system model. The algorithm computes these functions by evaluating the system's Jacobian matrices along simulation trajectories, eliminating the need for users to manually provide annotations while maintaining complete behavior coverage.
Solution Approach 2:
The patent performs preliminary computation of discrepancy functions by analyzing system dynamics before reachtube construction. By pre-computing the mathematical constructs needed for over-approximation from the system model itself, the method achieves complete behavior coverage without requiring user annotations during the reachtube computation phase.
Data Source
AI summary
A system and methods store initial states and unsafe states (e.g., safety requirements) of a non-linear model of a control system that interacts with a physical system. The system performs simulations of the non-linear model using a set of sampled initial states, to first generate trajectories (numerical approximations of actual behaviors) over bounded time. The system further determines, for respective pairs of neighboring trajectories: an over-approximation of reachable states as an upper bound of a distance between a pair of neighboring trajectories; a linear over-approximation of the reachable states as piece-wise linear segments over a plurality of time intervals; and whether the linear over-approximation overlaps in any of the piece-wise linear segments with the unsafe states, to verify the non-linear model of the control system is safe.