Compositional analysis for linear systems

Compositional analysis techniques such as assume-guarantee reasoning are frequently used in computer science to validate the design of complex process models. Since many engineering systems are built modularly from interconnections of components, the resulting mathematical models can be arbitrarily complex, which makes their analysis equally challenging. This paper presents a framework of how to apply compositional and assume-guarantee reasoning to linear time-invariant (LTI) systems. A key tool are simulation relations which are used to relate systems models with their specifications as well as to determine abstractions of given system behaviors. First, complex systems defined by standard feedback interconnections are considered. Parallel composition of LTI systems, the second type of interconnections, introduces algebraic constraints but allows for decomposition of a global specification.

[1]  Goran Frehse,et al.  Compositional verification of hybrid systems using simulation relations , 2005 .

[2]  Arjan van der Schaft,et al.  Assume-guarantee reasoning for linear dynamical systems , 2009, 2009 European Control Conference (ECC).

[3]  S. Shankar Sastry,et al.  Hierarchically consistent control systems , 2000, IEEE Trans. Autom. Control..

[4]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[5]  Arjan van der Schaft,et al.  Compositional analysis for linear control systems , 2010, HSCC '10.

[6]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[7]  George J. Pappas.  Bisimilar linear systems , 2003, Autom..

[8]  Arjan van der Schaft,et al.  Compositional and Assume-Guarantee Reasoning for Switching Linear Systems , 2009, ADHS.

[9]  Amir Pnueli,et al.  Revised Lectures from the International Symposium on Compositionality: The Significant Difference , 1997 .

[10]  Thomas A. Henzinger,et al.  You Assume, We Guarantee: Methodology and Case Studies , 1998, CAV.

[11]  A. J. van der Schaft.  Equivalence of dynamical systems by bisimulation , 2004, IEEE Transactions on Automatic Control.

[12]  Arjan van der Schaft,et al.  Equivalence of hybrid dynamical systems , 2004 .

[13]  K. Mani Chandy,et al.  Proofs of Networks of Processes , 1981, IEEE Transactions on Software Engineering.

[14]  Sérgio Vale Aguiar Campos,et al.  Compositional Reasoning in Model Checking , 1997, COMPOS.

[15]  Paulo Tabuada,et al.  Controller synthesis for bisimulation equivalence , 2007, Syst. Control. Lett..