Cyber-physical Systems

By definition, embedded systems interact directly with their environment. In many cases, the environment consists of analog behaviors that are determined by laws of physics. For this reason, the entire system, i.e. the environment together with the embedded system is a analog/digital system, also called a mixed-signal system in engineering, or a cyber-physical system in computer science (a generalization of classic hybrid systems of theoretical computer science). Such systems consist of finitely many discrete states, discrete variables and continuous variables. In each state, a set of differential equations determines the values of the continuous variables over time. Additionally, some conditions have to be regarded that are responsible to interrupt the continuous behavior associated with a state in that the system switches to another discrete state where other differential equations become valid. If such a discrete transition is made, the discrete variables can be given new values as well.

Modeling and analyzing cyber-physical systems recently received increased interest. It is clear that results in this area are very important for a complete analysis of an embedded system in its physical environment, but unfortunately most problems concerning cyber-physical systems turned out to be undecidable. For this reason, many restricted classes have been considered like rectangular and o-minimal systems.

Besides the difficulties in analysis, even modeling cyber-physical is more complicated than expected. Even though the essential paradigm is clear, there are not many programming languages with a precise semantics that could be used in a model-based design flow [CBPP04]. For this reason, we recently extended our formerly synchronous language Quartz by new kinds of variables and statements to describe cyber-physical systems as well. Our future work will cover the verification and analysis of thereby modeled cyber-physical systems.

References

			[CBPP04] L.P. Carloni and M.D. Di Benedetto and R. Passerone and A. Pinto and A. Sangiovanni-Vincentelli Modeling Techniques, Programming Languages, and Design Toolsets for Hybrid Systems
			[HKPV98] T.A. Henzinger and P.W. Kopke and A. Puri and P. Varaiya What's decidable about hybrid automata? Journal of Computer and System Sciences (JCSS)
			[ACHH93] R. Alur and C. Courcoubetis and T.A. Henzinger and P.-H. Ho Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems
			[ACHH95] R. Alur and C. Courcoubetis and N. Halbwachs and T.A. Henzinger and P. Ho and X. Nicollin and A. Olivero and J. Sifakis and S. Yovine The Algorithmic Analysis of Hybrid Systems Theoretical Computer Science (TCS)
			[RLSS10] R. Rajkumar and I. Lee and L. Sha and J. Stankovic Cyber physical systems: the next computing revolution Design Automation Conference (DAC)