Supervisory target control for hybrid systems

The problem of systematically synthesizing supervisory control laws that satisfy eventuality and efficiency requirements for hybrid systems modelled by hybrid automata is considered. Here, the efficiency requirement is specified by weighting the discrete transitions of the system. The optimization of the efficiency requirement is considered in the min-max sense due to the existence of disturbance inputs. Adopting a game theoretic approach, the high priority eventuality requirement is considered first and the class of controls, in which the low priority efficiency requirement should be optimized, is obtained. Then, a dynamic programming algorithm, which determines the value function of the optimization problem, is derived. A synthesis problem on a simplified batch process plant is considered to illustrate a potential application of the approach.

[1]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

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

[3]  C. SIAMJ.,et al.  MAXIMUM PRINCIPLE FOR A HYBRID SYSTEM VIA SINGULAR PERTURBATIONS∗ , 1999 .

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

[5]  H. Wong-Toi,et al.  The synthesis of controllers for linear hybrid automata , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

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

[7]  H. Sussmann,et al.  A maximum principle for hybrid optimal control problems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[8]  Karl Henrik Johansson,et al.  Dynamical Systems Revisited: Hybrid Systems with Zeno Executions , 2000, HSCC.

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

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

[11]  Thi Xuan Thao Dang.  Verification and Synthesis of Hybrid Systems , 2000 .

[12]  S. Sastry,et al.  On the existence of executions of hybrid automata , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[13]  Bengt Lennartson,et al.  Hybrid systems in process control , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[14]  B. Krogh,et al.  Synthesis of supervisory controllers for hybrid systems based on approximating automata , 1998, IEEE Trans. Autom. Control..

[15]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[16]  Eugene Asarin,et al.  As Soon as Possible: Time Optimal Control for Timed Automata , 1999, HSCC.

[17]  A. Trontis,et al.  Target control for hybrid systems with linear continuous dynamics , 2001 .

[18]  Thomas A. Henzinger,et al.  Automatic symbolic verification of embedded systems , 1993, 1993 Proceedings Real-Time Systems Symposium.

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

[20]  Alexandre M. Bayen,et al.  Validating a Hamilton-Jacobi Approximation to Hybrid System Reachable Sets , 2001, HSCC.

[21]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[22]  Yan Pang,et al.  Target control for hybrid systems , 2002 .

[23]  Pravin Varaiya,et al.  What's decidable about hybrid automata? , 1995, STOC '95.

[24]  A. Bensoussan,et al.  Hybrid control and dynamic programming , 1997 .

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

[26]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[27]  Hao Xia,et al.  Supervisory eventuality synthesis , 2002, Sixth International Workshop on Discrete Event Systems, 2002. Proceedings..

[28]  Bo Egardt,et al.  Control design for integrator hybrid systems , 1998, IEEE Trans. Autom. Control..

[29]  Olaf Stursberg,et al.  Verification of Logic Controllers for Continuous Plants , 1999 .

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

[31]  C SIAMJ.,et al.  AN OPTIMAL CONTROL THEORY FOR DISCRETE EVENT SYSTEMS , 1998 .

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

[33]  P.J. Antsaklis,et al.  Supervisory control of hybrid systems , 2000, Proceedings of the IEEE.

[34]  S. Shankar Sastry,et al.  O-Minimal Hybrid Systems , 2000, Math. Control. Signals Syst..

[35]  Pravin Varaiya,et al.  Ellipsoidal Techniques for Reachability Analysis , 2000, HSCC.

[36]  Gerardo Lafferriere,et al.  Symbolic Reachability Computation for Families of Linear Vector Fields , 2001, J. Symb. Comput..

[37]  S. Sastry,et al.  Zeno hybrid systems , 2001 .

[38]  Datta N. Godbole,et al.  Addressing Multiobjective Control: Safety and Performance through Constrained Optimization , 2001, HSCC.

[39]  Karl Henrik Johansson,et al.  Continuity and invariance in hybrid automata , 2001 .