A Fully Automated Framework for Control of Linear Systems from Temporal Logic Specifications

We consider the following problem: given a linear system and a linear temporal logic (LTL) formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula, and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using a procedure resembling model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included.

[1]  H. Raiffa,et al.  3. The Double Description Method , 1953 .

[2]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[3]  Pierre Wolper,et al.  Reasoning about infinite computation paths , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[4]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[5]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

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

[7]  G. Ziegler.  Lectures on Polytopes , 1994 .

[8]  Bud Mishra,et al.  Discrete event models+temporal logic=supervisory controller: automatic synthesis of locomotion controllers , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[9]  Pierre Wolper,et al.  Simple on-the-fly automatic verification of linear temporal logic , 1995, PSTV.

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

[11]  Benjamin Kuipers,et al.  Proving Properties of Continuous Systems: Qualitative Simulation and Temporal Logic , 1997, Artif. Intell..

[12]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[13]  Mireille E. Broucke.  A Geometric Approach to Bisimulation and Verification of Hybrid Systems , 1999, HSCC.

[14]  Giuseppe De Giacomo,et al.  Automata-Theoretic Approach to Planning for Temporally Extended Goals , 1999, ECP.

[15]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[16]  Doran Wilde,et al.  A LIBRARY FOR DOING POLYHEDRAL OPERATIONS , 2000 .

[17]  Pierre Wolper,et al.  Constructing Automata from Temporal Logic Formulas: A Tutorial , 2002, European Educational Forum: School on Formal Methods and Performance Analysis.

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

[19]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[20]  Jennifer M. Davoren,et al.  Robust Controller Synthesis for Hybrid Systems Using Modal Logic , 2001, HSCC.

[21]  Paul Gastin,et al.  Fast LTL to Büchi Automata Translation , 2001, CAV.

[22]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[23]  Samson Abramsky,et al.  Physical Traces: Quantum vs. Classical Information Processing , 2002, CTCS.

[24]  Paulo Tabuada,et al.  Bisimulation Relations for Dynamical and Control Systems , 2003, CTCS.

[25]  Ashish Tiwari,et al.  Series of Abstractions for Hybrid Automata , 2002, HSCC.

[26]  Gerard J. Holzmann,et al.  The SPIN Model Checker - primer and reference manual , 2003 .

[27]  Alberto Policriti,et al.  Foundations of a Query and Simulation System for the Modeling of Biochemical and Biological Processes , 2003, Pacific Symposium on Biocomputing.

[28]  Paulo Tabuada,et al.  Model Checking LTL over Controllable Linear Systems Is Decidable , 2003, HSCC.

[29]  George J. Pappas.  Bisimilar linear systems , 2003, Autom..

[30]  C. Belta,et al.  Constructing decidable hybrid systems with velocity bounds , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[31]  Thomas Bak,et al.  Planning : A Timed Automata Approach , 2004 .

[32]  Carl W. Lee,et al.  Subdivisions and Triangulationsof Polytopes , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[33]  K.J. Kyriakopoulos,et al.  Automatic synthesis of multi-agent motion tasks based on LTL specifications , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[34]  Jan H. van Schuppen,et al.  A control problem for affine dynamical systems on a full-dimensional polytope , 2004, Autom..

[35]  Thomas Bak,et al.  Multi-Robot Motion Planning: A Timed Automata Approach , 2004 .

[36]  Steven Fortune,et al.  Voronoi Diagrams and Delaunay Triangulations , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[37]  Nicolas Markey,et al.  Non-deterministic Temporal Logics for General Flow Systems , 2004, HSCC.

[38]  Thomas Brihaye,et al.  On O-Minimal Hybrid Systems , 2004, HSCC.

[39]  Giorgio Brajnik,et al.  Focusing qualitative simulation using temporal logic: theoretical foundations , 1998, Annals of Mathematics and Artificial Intelligence.

[40]  Radu Mateescu,et al.  Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in Escherichia coli , 2005, ISMB.

[41]  George J. Pappas,et al.  Hybrid Controllers for Path Planning: A Temporal Logic Approach , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[42]  Calin Belta,et al.  Discrete abstractions for robot motion planning and control in polygonal environments , 2005, IEEE Transactions on Robotics.

[43]  Calin Belta,et al.  Controlling a Class of Nonlinear Systems on Rectangles , 2006, IEEE Transactions on Automatic Control.

[44]  Calin Belta,et al.  Reachability Analysis of Multi-affine Systems , 2006, HSCC.

[45]  Calin Belta,et al.  Hierarchical abstractions for robotic swarms , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[46]  C. Belta,et al.  LTL Planning for Groups of Robots , 2006, 2006 IEEE International Conference on Networking, Sensing and Control.