Risk of Stochastic Systems for Temporal Logic Specifications

05/28/2022
by   Lars Lindemann, et al.
0

The wide availability of data coupled with the computational advances in artificial intelligence and machine learning promise to enable many future technologies such as autonomous driving. While there has been a variety of successful demonstrations of these technologies, critical system failures have repeatedly been reported. Even if rare, such system failures pose a serious barrier to adoption without a rigorous risk assessment. This paper presents a framework for the systematic and rigorous risk verification of systems. We consider a wide range of system specifications formulated in signal temporal logic (STL) and model the system as a stochastic process, permitting discrete-time and continuous-time stochastic processes. We then define the STL robustness risk as the risk of lacking robustness against failure. This definition is motivated as system failures are often caused by missing robustness to modeling errors, system disturbances, and distribution shifts in the underlying data generating process. Within the definition, we permit general classes of risk measures and focus on tail risk measures such as the value-at-risk and the conditional value-at-risk. While the STL robustness risk is in general hard to compute, we propose the approximate STL robustness risk as a more tractable notion that upper bounds the STL robustness risk. We show how the approximate STL robustness risk can accurately be estimated from system trajectory data. For discrete-time stochastic processes, we show under which conditions the approximate STL robustness risk can even be computed exactly. We illustrate our verification algorithm in the autonomous driving simulator CARLA and show how a least risky controller can be selected among four neural network lane keeping controllers for five meaningful system specifications.

READ FULL TEXT

page 1

page 10

research
04/03/2021

STL Robustness Risk over Discrete-Time Stochastic Processes

We present a framework to interpret signal temporal logic (STL) formulas...
research
08/30/2021

Reactive and Risk-Aware Control for Signal Temporal Logic

The deployment of autonomous systems in uncertain and dynamic environmen...
research
09/03/2013

On the Robustness of Temporal Properties for Stochastic Models

Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stoch...
research
02/18/2021

ReSonAte: A Runtime Risk Assessment Framework for Autonomous Systems

Autonomous CPSs are often required to handle uncertainties and self-mana...
research
09/25/2021

Verification of Switched Stochastic Systems via Barrier Certificates

The paper presents a methodology for temporal logic verification of cont...
research
06/08/2023

Combined Left and Right Temporal Robustness for Control under STL Specifications

Many modern autonomous systems, particularly multi-agent systems, are ti...
research
09/16/2022

Model Predictive Robustness of Signal Temporal Logic Predicates

The robustness of signal temporal logic not only assesses whether a sign...

Please sign up or login with your details

Forgot password? Click here to reset