HyTech : Hybrid Systems Analysis Using Interval Numerical Methods ? ? ?

Since hybrid embedded systems are pervasive and often safetycritical, guarantees about their correct performance are desirable. The hybrid systemsmodel checkerHyTech provides such guarantees and has successfully veri ed some systems. However, HyTech severely restricts the continuous dynamics of the system being analyzed and, therefore, often forces the use of prohibitively expensive discrete and polyhedral abstractions. We have designed a new algorithm, which is capable of directly verifying hybrid systems with general continuous dynamics, such as linear and nonlinear di erential equations. The new algorithm conservatively overapproximates the reachable states of a hybrid automaton by using interval numerical methods. Interval numerical methods return sets of points that enclose the true result of numerical computation and, thus, avoid distortions due to the accumulation of round-o errors. We have implemented the new algorithm in a successor tool to HyTech called HyperTech. We consider three examples: a thermostat with delay, a two-tank water system, and an air-tra c collision avoidance protocol. HyperTech enables the direct, fully automatic analysis of these systems, which is also more accurate than the use of polyhedral abstractions.