Symbolic models for nonlinear control systems affected by disturbances

References

• Alur , R and Dill , DL . 1990 . “ Automata, Languages and Programming ” . In Lecture Notes in Computer Science, in Automata for Modelling Real-time Systems , Edited by: Paterson , MS . Vol. 443 , 322 – 335 . Berlin : Springer .
   Google Scholar
• Alur , R , Henzinger , T , Kupferman , O and Vardi , M . 1998 . Alternating Refinement Relations . Proceedings of the 8th International Conference on Concurrence Theory, number 1466 in Lecture Notes in Computer Science, . 1998 . Edited by: Sangiorgi , D and de Simone , R . pp. 163 – 178 . Springer .
   Google Scholar
• Angeli , D . 2002 . A Lyapunov Approach to Incremental Stability Properties . IEEE Transactions on Automatic Control , 47 : 410 – 421 .
   Web of Science ®Google Scholar
• Angeli , D and Sontag , ED . 1999 . Forward Completeness, Unboundedness Observability, and their Lyapunov Characterisations . Systems and Control Letters , 38 : 209 – 217 .
   Web of Science ®Google Scholar
• Belta , C and Habets , LCGJM . 2006 . Controlling a Class of Nonlinear Systems on Rectangles . IEEE Transactions on Automatic Control , 51 : 1749 – 1759 .
   Web of Science ®Google Scholar
• Brihaye , T and Michaux , C . 2005 . On the Expressiveness and Decidability of O-minimal Hybrid Systems . Journal of Complexity , 21 : 447 – 478 .
   Web of Science ®Google Scholar
• Bicchi , A , Marigo , A and Piccoli , B . 2002 . On the Rechability of Quantized Control Systems . IEEE Transactions on Automatic Control , 47 : 546 – 563 .
   Web of Science ®Google Scholar
• Borri , A , Pola , G and Di Benedetto , MD . 2011 . Alternating Approximately Bisimilar Symbolic Models for Nonlinear Control Systems Affected by Disturbancess . 50th IEEE Conference on Decision and Control . 2011 . pp. 552 – 557 .
   Google Scholar
• Caines , PE and Wei , YJ . 1998 . Hierarchical Hybrid Control Systems: A Lattice-theoretic Formulation . Special Issue on Hybrid Systems, IEEE Transactions on Automatic Control , 43 : 501 – 508 .
   Web of Science ®Google Scholar
• Egerstedt , M , Frazzoli , E and Pappas , GJ . 2006 . Special Issue on Symbolic Methods for Complex Control Systems . IEEE Transactions on Automatic Control , 51 : 921 – 923 .
   Web of Science ®Google Scholar
• Forstner , D , Jung , M and Lunze , J . 2002 . A Discrete-event Model of Asynchronous Quantised Systems . Automatica , 38 : 1277 – 1286 .
   Web of Science ®Google Scholar
• Girard , A and Pappas , GJ . 2007 . Approximation Metrics for Discrete and Continuous Systems . IEEE Transactions on Automatic Control , 52 : 782 – 798 .
   Web of Science ®Google Scholar
• Girard , A , Pola , G and Tabuada , P . 2010 . Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems . IEEE Transactions of Automatic Control , 55 : 116 – 126 .
   Web of Science ®Google Scholar
• Habets , LCGJM , Collins , PJ and van Schuppen , JH . 2006 . Reachability and Control Synthesis for Piecewise-affine Hybrid Systems on Simplices . IEEE Transactions on Automatic Control , 51 : 938 – 948 .
   Web of Science ®Google Scholar
• Henzinger , TA , Kopke , PW , Puri , A and Varaiya , P . 1998 . What's Decidable about Hybrid Automata? . Journal of Computer and System Sciences , 57 : 94 – 124 .
   Web of Science ®Google Scholar
• Junge , O . 2004 . A Set Oriented Approach to Global Optimal Control . ESAIM: Control, optimisation and calculus of variations , 10 : 259 – 270 .
   Web of Science ®Google Scholar
• Koutsoukos , XD , Antsaklis , PJ , Stiver , JA and Lemmon , MD . 2000 . Supervisory Control of Hybrid Systems . in Proceedings of the IEEE , 88 : 1026 – 1049 .
   Web of Science ®Google Scholar
• Khalil , HK . 1996 . Nonlinear Systems , 2nd , New Jersey : Prentice Hall .
   Google Scholar
• Lafferriere , G , Pappas , GJ and Sastry , S . 2000 . O-minimal Hybrid Systems . Mathematical Control Signal Systems , 13 : 1 – 21 .
   Web of Science ®Google Scholar
• Milner , R . 1989 . Communication and Concurrency , Upper Saddle River, NJ , , USA : Prentice Hall .
   Google Scholar
• Moor , T , Raisch , J and O'Young , SD . 2002 . Discrete Supervisory Control of Hybrid Systems Based on L-complete Approximations . Journal of Discrete Event Dynamic Systems , 12 : 83 – 107 .
   Web of Science ®Google Scholar
• Nesic , D and Teel , AR . 2001 . “ Sampled-data Control of Nonlinear Systems: An Overview of Recent Results ” . In Perspectives on Robust Control , Edited by: Moheimani , RSO . 221 – 239 . New York : Springer-Verlag .
   Google Scholar
• Park , DMR . 1981 . Concurrency and Automata on Infinite Sequences . Lecture Notes in Computer Science , 104 : 167 – 183 .
   Google Scholar
• Pola , G , Borri , A and Di Benedetto , MD . 2012 . Integrated Design of Symbolic Controllers for Nonlinear Systems . IEEE Transactions on Automatic Control , 57 : 534 – 539 .
   Web of Science ®Google Scholar
• Pola , G , Girard , A and Tabuada , P . 2008 . Approximately Bisimilar Symbolic Models for Nonlinear Control Systems . Automatica , 44 : 2508 – 2516 .
   Web of Science ®Google Scholar
• Pola , G , Pepe , P and Di Benedetto , MD . 2010a . Alternating Approximately Bisimilar Symbolic Models for Nonlinear Control Systems with Unknown Time-varying Delays . 49th IEEE Conference on Decision and Control (CDC) . 2010a . pp. 7649 – 7654 .
   Google Scholar
• Pola , G , Pepe , P , Di Benedetto , MD and Tabuada , P . 2010b . Symbolic Models for Nonlinear Time-delay Systems using Approximate Bisimulations . Systems and Control Letters , 59 : 365 – 373 .
   Web of Science ®Google Scholar
• Pola , G and Tabuada , P . 2009 . Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations . SIAM Journal on Control and Optimization , 48 : 719 – 733 .
   Web of Science ®Google Scholar
• Reißig , G . 2009 . Computation of Discrete Abstractions of Arbitrary Memory Span for Nonlinear Sampled Systems . Proceedings of 12th International Conference Hybrid Systems: Computation and Control (HSCC) . 2009 . Vol. 5469 , pp. 306 – 320 .
   Google Scholar
• Schultz , MH . 1973 . Spline Analysis , Englewood Cliffs, New Jersey : Prentice Hall .
   Google Scholar
• Sontag , ED . 1998 . “ Mathematical Control Theory ” . In in Texts in Applied Mathematics , 2nd , Vol. 6 , New York : Springer-Verlag .
   Google Scholar
• Tabuada , P . 2009 . Verification and Control of Hybrid Systems: A Symbolic Approach , Heidelberg : Springer .
   Google Scholar
• Zamani , M , Mazo , M , Pola , G and Tabuada , P . 2012 . Symbolic Models for Nonlinear Control Systems without Stability Assumptions . IEEE Transactions of Automatic Control , In press, DOI: 10.1109/TAC.2011.2176409
   Web of Science ®Google Scholar