Periodically-Scheduled Controller Analysis Using Hybrid Systems Reachability and Continuization

Abstract

Cyber-physical systems (CPS) consist of physical entities that obey dynamical laws and interact with software components. A typical CPS implementation includes a discrete controller, where software periodically samples physical state and produces actuation commands according to a real-time schedule. Such a hybrid system can be modeled formally as a hybrid automaton. However, reachability tools to verify specifications for hybrid automata do not perform well on such periodicallyscheduled models. This is due to a combination of the large number of discrete jumps and the nondeterminism of the exact controller start time. In this paper, we demonstrate this problem and propose a solution, which is a validated abstraction mechanism where every behavior of the original sampled system is contained in the behaviors of a purely continuous system with an additive nondeterministic input. Reachability tools for hybrid automata can better handle such systems. We further improve the analysis by considering local analysis domains. We automate the proposed technique in the Hyst model transformation tool, and demonstrate its effectiveness in a case study analyzing the design of a yaw-damper for a jet aircraft.

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

“…Continuization methods [3,4,12] eliminate intersections using abstractions that get rid of fast-switching dynamics or eliminate guard intersections between similar continuous dynamics, as performed for m either in this work. Frehse et al [30] cast the intersection operator as a convex minimization problem.…”

Charge Pump Phase-Locked Loops and Full Wave Rectifiers for Reachability Analysis

“…It is pertinent to highlight that in [4], the authors have used a variant of continuization [1] to address this problem for the design of a yaw damper system for a 747 jet aircraft. Continuization is a process whereby the abstraction of a hybrid system having large number of discrete transitions is obtained by a continuous system with an extra non-deterministic input.…”

“…Continuization is a process whereby the abstraction of a hybrid system having large number of discrete transitions is obtained by a continuous system with an extra non-deterministic input. The authors use HyST to automatically transform the model and perform reachability analysis using Flow* and SpaceEx to display satisfactory results in [4]. A similar approach can be used for this benchmark so as to perform reachability analysis using SpaceEx and Flow*.…”

“…Therefore, the SpaceEx analysis did not produce accurate reachability results if the analysis is run for an extended duration of time. This requires some advanced techniques, such as continuization [1] that is demostarted in [4] using HyST, SpaceEx, and Flow*. For FWR, SpaceEx produced a run-time error due to non-affine dynamics as the model had pure sinusoidal time-dependent signal as an input.…”

Model-based compositional verification approaches and tools development for cyber-physical systems

“…Improvement has been done on eliminating spurious discrete transitions caused by conservative over-approximation involving template polyhedra, and checking the existence of a hyperplane that separates the guard set from the flowpipe [30]. A model translation technique implemented by Hyst [31,32] is used to alleviate the same problem using a different approach. Hyst over-approximates the original frequently switching continuously-controlled system with a continuously-controlled system with an additional bounded non-deterministic input, resulting in the so-called continuization, which eliminates a large number of discrete transitions, thereby eliminating error growth caused by frequent translations between the aforementioned two types of representations occurring at the discrete transitions.…”