Low-Complexity Switching Controllers for Safety using Symbolic Models

In this paper, we consider the problem of synthesizing low-complexity safety controllers for incrementally stable switched systems. For that purpose, we establish a new approximation result for the computation of symbolic models that are approximately bisimilar to a given switched system. The main advantage over existing results is that it allows us to design quantized switching controllers for safety specifications; these can be computed offline and therefore the online execution time is greatly reduced. Then, we present a technique to reduce the memory needed to store the control law by borrowing ideas from algebraic decision diagrams for compact function representation and by exploiting the non-determinism inherent to safety controllers. We show the merits of our approach by applying it to a simple model of temperature regulation in a building.

[1]  Calin Belta,et al.  A Fully Automated Framework for Control of Linear Systems from LTL Specifications , 2006, HSCC.

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

[3]  Jun-ichi Imura,et al.  Finite Abstractions of Discrete-time Linear Systems and Its Application to Optimal Control , 2008 .

[4]  Sean P. Meyn,et al.  Building thermal model reduction via aggregation of states , 2010, Proceedings of the 2010 American Control Conference.

[5]  Antoine Girard,et al.  Safety controller synthesis for switched systems using multi-scale symbolic models , 2011, IEEE Conference on Decision and Control and European Control Conference.

[6]  R. I. Bahar,et al.  Algebraic decision diagrams and their applications , 1993, Proceedings of 1993 International Conference on Computer Aided Design (ICCAD).

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

[8]  David Angeli,et al.  A Lyapunov approach to incremental stability properties , 2002, IEEE Trans. Autom. Control..

[9]  P Tabuada,et al.  Approximate time-optimal control via approximate alternating simulations , 2010, Proceedings of the 2010 American Control Conference.

[10]  Paulo Tabuada,et al.  Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations , 2007, SIAM J. Control. Optim..

[11]  Jörg Raisch,et al.  Discrete approximation and supervisory control of continuous systems , 1998, IEEE Trans. Autom. Control..

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

[13]  Jörg Raisch,et al.  Supervisory control of hybrid systems within a behavioural framework , 1999 .

[14]  Gunther Reissig.  Computation of Discrete Abstractions of Arbitrary Memory Span for Nonlinear Sampled Systems , 2009, HSCC.

[15]  Antoine Girard,et al.  Controller synthesis for safety and reachability via approximate bisimulation , 2010, Autom..

[16]  Antoine Girard,et al.  Approximation Metrics for Discrete and Continuous Systems , 2006, IEEE Transactions on Automatic Control.

[17]  Paulo Tabuada,et al.  Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems , 2008, IEEE Transactions on Automatic Control.