Semi-decidable Synthesis for Triangular Hybrid Systems

The algorithmic design of least restrictive controllers for hybrid systems that satisfy reachability specifications has received much attention recently. Despite the importance of algorithmic approaches to controller design for hybrid systems, results that guarantee termination of the algorithms have been limited. In this paper, we extend recent decidability results on controller synthesis for classes of linear hybrid systems to semi-decision procedures for triangular hybrid systems which can be used to model nonholonomic systems after a transformation. Our results are then applied to verification of a conflict resolution maneuver from air traffic control.

[1]  Oded Maler,et al.  Reachability Analysis via Face Lifting , 1998, HSCC.

[2]  S. Shankar Sastry,et al.  Conflict resolution for air traffic management: a study in multiagent hybrid systems , 1998, IEEE Trans. Autom. Control..

[3]  Gerardo Lafferriere,et al.  A New Class of Decidable Hybrid Systems , 1999, HSCC.

[4]  A. Pnueli,et al.  Effective synthesis of switching controllers for linear systems , 2000, Proceedings of the IEEE.

[5]  John Lygeros,et al.  Computing Controllers for Nonlinear Hybrid Systems , 1999, HSCC.

[6]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[7]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[8]  A. Tarski A Decision Method for Elementary Algebra and Geometry , 2023 .

[9]  Ian M. Mitchell,et al.  Level Set Methods for Computation in Hybrid Systems , 2000, HSCC.

[10]  J. Canny,et al.  Nonholonomic Motion Planning , 1992 .

[11]  S. Shankar Sastry,et al.  Semidecidable controller synthesis for classes of linear hybrid systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[12]  S. Shankar Sastry,et al.  Decidable Controller Synthesis for Classes of Linear Systems , 2000, HSCC.

[13]  John Lygeros,et al.  Controllers for reachability specifications for hybrid systems , 1999, Autom..

[14]  Bruce H. Krogh,et al.  Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations , 1999, HSCC.