Safety Control of Hidden Mode Hybrid Systems

In this paper, we consider the safety control problem for hidden mode hybrid systems (HMHSs), which are a special class of hybrid automata in which the mode is not available for control. For these systems, safety control is a problem with imperfect state information. We tackle this problem by introducing the notion of nondeterministic discrete information state and by translating the problem to one with perfect state information. The perfect state information control problem is obtained by constructing a new hybrid automaton, whose discrete state is an estimate of the HMHS mode and is, as such, available for control. This problem is solved by computing the capture set and the least restrictive control map for the new hybrid automaton. Sufficient conditions for the termination of the algorithm that computes the capture set are provided. Finally, we show that the solved perfect state information control problem is equivalent to the original problem with imperfect state information under suitable assumptions. We illustrate the application of the proposed technique to a collision avoidance problem between an autonomous vehicle and a human driven vehicle at a traffic intersection.

[1]  Don-Ha Hwang,et al.  Modeling of Human Driving Behavior Based on Piecewise Linear Model , 2005, Proceedings of the IEEE International Symposium on Industrial Electronics, 2005. ISIE 2005..

[2]  Domitilla Del Vecchio.  Observer-based control of block-triangular discrete time hybrid automata on a partial order† , 2009 .

[3]  S. Shankar Sastry,et al.  Aircraft conflict prediction in the presence of a spatially correlated wind field , 2005, IEEE Transactions on Intelligent Transportation Systems.

[4]  Alberto L. Sangiovanni-Vincentelli,et al.  Design of Observers for Hybrid Systems , 2002, HSCC.

[5]  P. Varaiya,et al.  Ellipsoidal Techniques for Hybrid Dynamics: the Reachability Problem , 2005 .

[6]  L. Blackmore,et al.  Active Estimation for Switching Linear Dynamic Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[7]  Giorgio Battistelli,et al.  Active mode observability of switching linear systems , 2007, Autom..

[8]  S. Shankar Sastry,et al.  Semi-decidable Synthesis for Triangular Hybrid Systems , 2001, HSCC.

[9]  Jean-François Raskin,et al.  A Lattice Theory for Solving Games of Imperfect Information , 2006, HSCC.

[10]  Domitilla Del Vecchio,et al.  Continuous control of hybrid automata with imperfect mode information assuming separation between state estimation and control , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[11]  David Angeli,et al.  Interconnections of Monotone Systems with Steady-State Characteristics , 2004 .

[12]  Maria Domenica Di Benedetto,et al.  Computation of maximal safe sets for switching systems , 2004, IEEE Transactions on Automatic Control.

[13]  Anna Philippou,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2018, Lecture Notes in Computer Science.

[14]  Yiannis Demiris,et al.  Prediction of intent in robotics and multi-agent systems , 2007, Cognitive Processing.

[15]  D. Del Vecchio,et al.  Development of a Scaled Vehicle With Longitudinal Dynamics of an HMMWV for an ITS Testbed , 2008, IEEE/ASME Transactions on Mechatronics.

[16]  Domitilla Del Vecchio,et al.  Formal design of a provably safe robotic roundabout system , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[17]  Thomas A. Henzinger,et al.  A User Guide to HyTech , 1995, TACAS.

[18]  David Angeli,et al.  Oscillations in I/O Monotone Systems Under Negative Feedback , 2007, IEEE Transactions on Automatic Control.

[19]  R. Vidal,et al.  Observability and identifiability of jump linear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[20]  Jörn Pachl,et al.  Railway Operation and Control , 2002 .

[21]  Jean-Pierre Aubin,et al.  Impulse differential inclusions: a viability approach to hybrid systems , 2002, IEEE Trans. Autom. Control..

[22]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[23]  J. Ragot,et al.  Active Mode Estimation for Switching Systems , 2007, 2007 American Control Conference.

[24]  Domitilla Del Vecchio.  A Partial Order Approach to Discrete Dynamic Feedback in a Class of Hybrid Systems , 2007, HSCC.

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

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

[27]  Domitilla Del Vecchio.  Cascade estimators for systems on a partial order , 2008, Syst. Control. Lett..

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

[29]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[30]  John H. Reif,et al.  The Complexity of Two-Player Games of Incomplete Information , 1984, J. Comput. Syst. Sci..

[31]  D. Del Vecchio,et al.  Observation of guarded command programs , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[32]  Domitilla Del Vecchio,et al.  A separation principle for a class of hybrid automata on a partial order , 2009, 2009 American Control Conference.

[33]  P. Perona,et al.  Primitives for Human Motion: a Dynamical Approach , 2002 .

[34]  R. D'Andrea,et al.  RoboFlag games using systems based, hierarchical control , 2003, Proceedings of the 2003 American Control Conference, 2003..

[35]  Richard M. Murray,et al.  Discrete state estimators for systems on a lattice , 2006, Autom..

[36]  Inseok Hwang,et al.  Terminal-Area Aircraft Tracking Using Hybrid Estimation , 2009 .

[37]  Alexandre M. Bayen,et al.  A Cooperative Distributed Approach to Multi-Agent Eulerian Network Control: Application to Air Traffic Management ∗ , 2005 .

[38]  Domitilla Del Vecchio,et al.  Computation of safety control for uncertain piecewise continuous systems on a partial order , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[39]  Amir Pnueli,et al.  Symbolic Controller Synthesis for Discrete and Timed Systems , 1994, Hybrid Systems.

[40]  Alexandre M. Bayen,et al.  Invariance-Preserving Abstractions of Hybrid Systems: Application to User Interface Design , 2008, IEEE Transactions on Control Systems Technology.

[41]  Jean-Pierre Aubin,et al.  Viability theory , 1991 .

[42]  Domitilla Del Vecchio,et al.  Partial order techniques for vehicle collision avoidance: Application to an autonomous roundabout test-bed , 2009, 2009 IEEE International Conference on Robotics and Automation.

[43]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[44]  H. W. Kuhn,et al.  11. Extensive Games and the Problem of Information , 1953 .

[45]  Sorin Istrail,et al.  Generalization of the Ginsburg-Rice Schützenberger Fixed-Point Theorem for Context-Sensitive and Recursive-Enumerable Languages , 1982, Theor. Comput. Sci..

[46]  Pietro Perona,et al.  Decomposition of human motion into dynamics-based primitives with application to drawing tasks , 2003, Autom..

[47]  Tuomas Sandholm,et al.  Solving two-person zero-sum repeated games of incomplete information , 2008, AAMAS.

[48]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[49]  Alexandre M. Bayen,et al.  Computational techniques for the verification of hybrid systems , 2003, Proc. IEEE.

[50]  Robert J. Aumann,et al.  Repeated Games with Incomplete Information , 1995 .

[51]  Yan Gao,et al.  The Reachability Problem for Uncertain Hybrid Systems Revisited: A Viability Theory Perspective , 2006, HSCC.

[52]  R. J. Hill.  Electric railway traction. I. Electric traction and DC traction motor drives , 1994 .

[53]  J. Lygeros,et al.  A game theoretic approach to controller design for hybrid systems , 2000, Proceedings of the IEEE.

[54]  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).

[55]  Thomas A. Henzinger,et al.  Beyond HYTECH: Hybrid Systems Analysis Using Interval Numerical Methods , 2000, HSCC.