An Approximate Simulation Approach to Symbolic Control

This paper introduces a methodology for the symbolic control of nonlinear systems based on an approximate notion of simulation relation. This notion generalizes existing exact notions of simulation and is completely characterized in terms of known stabilizability concepts. Equipped with this notion we show how, under certain stabilizability assumptions, we can construct finite or symbolic models for nonlinear control systems. Synthesizing controllers for the original control system can then be done by using supervisory control techniques on the finite models and by refining the resulting finite controllers to hybrid controllers enforcing the specification on the original continuous control system. The proposed design methodology can be seen as a correct-by-design way of obtaining both the feedback control laws as well as the control software responsible for deciding which law is executed and when.

[1]  Jörg Raisch,et al.  Discrete Supervisory Control of Hybrid Systems Based on l-Complete Approximations , 2002, Discret. Event Dyn. Syst..

[2]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[3]  A. Bacciotti,et al.  Liapunov functions and stability in control theory , 2001 .

[4]  Yuandan Lin,et al.  A Smooth Converse Lyapunov Theorem for Robust Stability , 1996 .

[5]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[6]  Paulo Tabuada.  Symbolic control of linear systems based on symbolic subsystems , 2006, IEEE Transactions on Automatic Control.

[7]  George J. Pappas,et al.  Approximate Bisimulations for Nonlinear Dynamical Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[8]  Robert L. Grossman,et al.  Timed Automata , 1999, CAV.

[9]  Paulo Tabuada,et al.  Symbolic models for control systems , 2007, Acta Informatica.

[10]  Antonio Bicchi,et al.  On the reachability of quantized control systems , 2002, IEEE Trans. Autom. Control..

[11]  Eduardo D. Sontag,et al.  Control-Lyapunov Universal Formulas for Restricted Inputs , 1995 .

[12]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[13]  Munther A. Dahleh,et al.  Maneuver-based motion planning for nonlinear systems with symmetries , 2005, IEEE Transactions on Robotics.

[14]  Antonio Bicchi,et al.  Optimal Control of Quantized Input Systems , 2002, HSCC.

[15]  Vijay K. Garg,et al.  Modeling and Control of Logical Discrete Event Systems , 1994 .

[16]  Z. Artstein.  Stabilization with relaxed controls , 1983 .

[17]  Antonio Bicchi,et al.  Feedback encoding for efficient symbolic control of dynamical systems , 2006, IEEE Transactions on Automatic Control.

[18]  Panos J. Antsaklis,et al.  Linear Systems , 1997 .

[19]  S. Shankar Sastry,et al.  Mode Switching Synthesis for Reachability Specifications , 2001, HSCC.

[20]  Elena Panteley,et al.  Exponential tracking control of a mobile car using a cascaded approach , 1998 .

[21]  Paulo Tabuada,et al.  Linear Time Logic Control of Discrete-Time Linear Systems , 2006, IEEE Transactions on Automatic Control.

[22]  George J. Pappas,et al.  Approximate Bisimulations for Constrained Linear Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.