Hybrid Decentralized Control of Large Scale Systems

Motivated by three applications which are under investigation at the Honeywell Research Laboratory in Minneapolis, we introduce a class of large scale control problems. In particular we show that a formation flight problem, a paper machine control problem and the coordination of cameras in a monitoring network can be cast into this class. In the second part of the paper we propose a decentralized control scheme to tackle the complexity of the problem. The scheme makes use of logic rules which improve stability and feasibility of the decentralized method by enforcing coordination. The decentralized control laws which respect the rules are computed using hybrid control design.

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

[2]  Joao P. Hespanha,et al.  Logic-based switching control for trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty , 2004, Proceedings of the 2004 American Control Conference.

[3]  Panos J. Antsaklis,et al.  Special issue on hybrid systems: theory and applications a brief introduction to the theory and applications of hybrid systems , 2000, Proc. IEEE.

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

[5]  Michael S. Branicky,et al.  Studies in hybrid systems: modeling, analysis, and control , 1996 .

[6]  Alberto Bemporad,et al.  Observability and controllability of piecewise affine and hybrid systems , 2000, IEEE Trans. Autom. Control..

[7]  John N. Tsitsiklis,et al.  A survey of computational complexity results in systems and control , 2000, Autom..

[8]  F. Borrelli,et al.  Collision-free UAV formation flight using decentralized optimization and invariant sets , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[9]  Arjan van der Schaft,et al.  Complementarity modelling of hybrid systems , 1997 .

[10]  John Lygeros,et al.  A Game-Theoretic Approach to Hybrid System Design , 1996, Hybrid Systems.

[11]  Magnus Egerstedt,et al.  Conflict Resolution for Autonomous Vehicles: A Case Study in Hierarchical Control Design , 2002 .

[12]  S. Lall,et al.  Decentralized control information structures preserved under feedback , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[13]  Jonathan P. How,et al.  Aircraft trajectory planning with collision avoidance using mixed integer linear programming , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

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

[15]  Antonio Bicchi,et al.  On optimal cooperative conflict resolution for air traffic management systems , 2000, IEEE Trans. Intell. Transp. Syst..

[16]  Dimitry M. Gorinevsky,et al.  Feedback controller design for a spatially distributed system: the paper machine problem , 2003, IEEE Trans. Control. Syst. Technol..

[17]  William B. Dunbar,et al.  Cooperative control of multi-vehicle systems using cost graphs and optimization , 2003, Proceedings of the 2003 American Control Conference, 2003..

[18]  T. Keviczky,et al.  Hierarchical design of decentralized receding horizon controllers for decoupled systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[19]  R.M. Murray,et al.  On the synthesis of control laws for a network of autonomous agents , 2004, Proceedings of the 2004 American Control Conference.

[20]  Jonathan P. How,et al.  COORDINATION AND CONTROL OF MULTIPLE UAVs , 2002 .

[21]  E. Davison,et al.  On the stabilization of decentralized control systems , 1973 .

[22]  Bonaventure Intercontinental,et al.  ON DECISION AND CONTROL , 1985 .

[23]  Kevin Wise Control in an Information Rich World , 2001 .

[24]  Mario Innocenti,et al.  Autonomous formation flight , 2000 .

[25]  R.M. Murray,et al.  Receding horizon control of multi-vehicle formations: a distributed implementation , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[26]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..

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

[28]  F. Borrelli,et al.  A study on decentralized receding horizon control for decoupled systems , 2004, Proceedings of the 2004 American Control Conference.

[29]  Francesco Borrelli,et al.  Constrained Optimal Control of Linear and Hybrid Systems , 2003, IEEE Transactions on Automatic Control.

[30]  R. D’Andrea,et al.  Exploiting symmetry for the distributed control of spatially interconnected systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[31]  J. M. Davoren Logic-based design and synthesis of controllers for hybrid systems , 2007 .

[32]  M. Egerstedt,et al.  How hard is it to control switched systems? , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[33]  David Q. Mayne,et al.  Control of Constrained Dynamic Systems , 2001, Eur. J. Control.

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

[35]  A. Richards,et al.  A decentralized algorithm for robust constrained model predictive control , 2004, Proceedings of the 2004 American Control Conference.

[36]  Richard D. Braatz,et al.  Identification and Control of Sheet and Film Processes , 2000 .

[37]  William B. Dunbar,et al.  Model predictive control of coordinated multi-vehicle formations , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[38]  Thomas A. Henzinger,et al.  Hybrid Systems III , 1995, Lecture Notes in Computer Science.

[39]  Eduardo Camponogara,et al.  Distributed model predictive control , 2002 .

[40]  Rodney Teo,et al.  Decentralized overlapping control of a formation of unmanned aerial vehicles , 2004, Autom..

[41]  Albert Benveniste,et al.  Markov nets: probabilistic models for distributed and concurrent systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[42]  Xiaoming Hu,et al.  A control Lyapunov function approach to multiagent coordination , 2002, IEEE Trans. Robotics Autom..

[43]  Francesco Borrelli,et al.  A comparison between Mixed Integer Programming and Nonlinear Programming Techniques for 3 D Conflict Resolution of Multiple Aircraft , 2003 .

[44]  Geir E. Dullerud,et al.  Distributed control design for spatially interconnected systems , 2003, IEEE Trans. Autom. Control..

[45]  S. Shankar Sastry,et al.  Decentralized nonlinear model predictive control of multiple flying robots , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[46]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[47]  Petter Ögren,et al.  A control Lyapunov function approach to multi-agent coordination , 2001 .

[48]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..