Receding Horizon Control of a two-agent system with competitive objectives

We consider the problem of controlling two dynamically decoupled agents which can cooperate or compete. Agents are modelled as linear discrete time systems, and collect each other's state information without delays. Control actions are computed using a Receding Horizon framework, where each agent's controllers are computed by minimizing a linear, quadratic cost function which depends on both agents' states. Cooperation or competition is specified throught the state tracking objectives of each agent. We do not consider state constraints. The simplicity of our framework allows us to provide the following results analytically: 1) When agents compete, their states converge to an equilibrium trajectory where the steady state tracking error is finite. 2) Limit-cycles cannot occur. Numerical simulations and experiments done with a LEGO Mindstorm multiagent platform match our analytical results.

[1]  James C. Hung.  Dynamic Matrix Control , 2011 .

[2]  K. Miller.  On the Inverse of the Sum of Matrices , 1981 .

[3]  Philippe Poignet,et al.  Moving horizon control for biped robots without reference trajectory , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[4]  William B. Dunbar,et al.  Distributed Model Predictive Control for Dynamic Supply Chain Management , 2005 .

[5]  Robert R. Bitmead,et al.  Adaptive optimal control , 1990 .

[6]  William B. Dunbar,et al.  Distributed receding horizon control for multi-vehicle formation stabilization , 2006, Autom..

[7]  R. Beck,et al.  Model Predictive Control of a Parallel Hybrid Vehicle Drivetrain , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[8]  John R. Hauser,et al.  Applied receding horizon control of the Caltech Ducted Fan , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[9]  Sigurd Skogestad,et al.  Control structure design for complete chemical plants , 2004, Comput. Chem. Eng..

[10]  Alberto Bemporad,et al.  An MPC/hybrid system approach to traction control , 2006, IEEE Transactions on Control Systems Technology.

[11]  William F. Trench,et al.  Inverses of lower triangular Toeplitz matrices , 2009 .

[12]  J.P. Hespanha,et al.  Multiple-agent probabilistic pursuit-evasion games , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[13]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..

[14]  Maria Domenica Di Benedetto,et al.  Hide-and-Seek with Directional Sensing , 2011, ArXiv.

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

[16]  S. Shankar Sastry,et al.  Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation , 2002, IEEE Trans. Robotics Autom..

[17]  Marios M. Polycarpou,et al.  Design and stability analysis of cooperative receding‐horizon control of linear discrete‐time agents , 2007 .

[18]  J. Richalet,et al.  Model predictive heuristic control: Applications to industrial processes , 1978, Autom..

[19]  Ryota Ishibashi,et al.  A modeling of pedestrian behavior based on hybrid systems approach — An analysis on the direction of confluence , 2011, SICE Annual Conference 2011.

[20]  Marko Bacic,et al.  Model predictive control , 2003 .

[21]  Andrea Carron,et al.  Receding Horizon Control of Multiagents Systems with Competitive Dynamics , 2012 .

[22]  T. Parisini,et al.  Cooperative control of discrete-time agents with delayed information exchange: A receding-horizon approach , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).