On compositional symbolic controller synthesis inspired by small-gain theorems

In this paper, we present a compositional method for the synthesis of controllers enforcing persistency specifications. This method is inspired by two classes of compositional techniques: small-gain theorems from the control literature; and assume-guarantee reasoning from the formal methods literature. We show that the method presented in this paper is strictly more general than a representative existing small-gain theorem.

[1]  Martín Abadi,et al.  Conjoining specifications , 1995, TOPL.

[2]  Sagar Chaki,et al.  Assume-Guarantee Reasoning for Deadlock , 2006, 2006 Formal Methods in Computer Aided Design.

[3]  Dragan Nesic,et al.  Discrete-time Lyapunov-based small-gain theorem for parameterized interconnected ISS systems , 2003, IEEE Trans. Autom. Control..

[4]  Antoine Girard,et al.  CoSyMA: a tool for controller synthesis using multi-scale abstractions , 2013, HSCC '13.

[5]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[6]  Pierre Wolper,et al.  Reasoning about infinite computation paths , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[7]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[8]  Patrick Maier A Set-Theoretic Framework for Assume-Guarantee Reasoning , 2001, ICALP.

[9]  Kenneth L. McMillan,et al.  Circular Compositional Reasoning about Liveness , 1999, CHARME.

[10]  Zhong-Ping Jiang,et al.  A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems , 1996, Autom..

[11]  Ufuk Topcu,et al.  TuLiP: a software toolbox for receding horizon temporal logic planning , 2011, HSCC '11.

[12]  Paulo Tabuada,et al.  Verification and Control of Hybrid Systems , 2009 .

[13]  Paulo Tabuada,et al.  Verification and Control of Hybrid Systems - A Symbolic Approach , 2009 .

[14]  Mahesh Viswanathan,et al.  Foundations for Circular Compositional Reasoning , 2001, ICALP.

[15]  Thomas A. Henzinger,et al.  Reactive Modules , 1999, Formal Methods Syst. Des..

[16]  Thomas A. Henzinger,et al.  Decomposing refinement proofs using assume-guarantee reasoning , 2000, IEEE/ACM International Conference on Computer Aided Design. ICCAD - 2000. IEEE/ACM Digest of Technical Papers (Cat. No.00CH37140).

[17]  A. Teel A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

[18]  Manuel Mazo,et al.  PESSOA: A Tool for Embedded Controller Synthesis , 2010, CAV.

[19]  Kedar S. Namjoshi,et al.  On the completeness of compositional reasoning methods , 2010, TOCL.