A Risk-Averse Differential Game Approach to Multi-agent Tracking and Synchronization with Stochastic Objects and Command Generators

This chapter presents the formulation of a class of distributed stochastic multi-agent systems where local interconnections among cautious and defensive decision makers and/or trackers are supported by connectivity graphs. Associated with autonomous decision makers and/or trackers are finite-horizon performance measures for conflict-free coordination and cohesive object and/or command tracking. The current analysis is limited to the class of distributed linear stochastic systems and measurement subsystems. It is shown that optimal rules for ordering uncertain prospects are feasible for all self-directed decision makers and/or trackers with output-feedback Nash decision making and risk-averse utility functions.

[1]  T. Başar,et al.  Dynamic Noncooperative Game Theory, 2nd Edition , 1998 .

[2]  Khanh Pham,et al.  Non-Cooperative Outcomes for Stochastic Nash Games: Decision Strategies towards Multi-Attribute Performance Robustness , 2008 .

[3]  A. Friedman.  Foundations of modern analysis , 1970 .

[4]  Genshe Chen,et al.  A trust-based sensor allocation algorithm in cooperative space search problems , 2011, Defense + Commercial Sensing.

[5]  K. D. Pham.  Performance-Reliability-Aided Decision-Making in Multiperson Quadratic Decision Games Against Jamming and Estimation Confrontations , 2011, J. Optim. Theory Appl..

[6]  Ming Xin,et al.  Multi-agent consensus algorithm with obstacle avoidance via optimal control approach , 2011, Proceedings of the 2011 American Control Conference.

[7]  Alexander Pollatsek,et al.  A theory of risk , 1970 .

[8]  T. Başar.  Nash Equilibria of Risk-Sensitive Nonlinear Stochastic Differential Games , 1999 .

[9]  P. Whittle.  Risk-Sensitive Optimal Control , 1990 .

[10]  Dongbing Gu,et al.  A Differential Game Approach to Formation Control , 2008, IEEE Transactions on Control Systems Technology.

[11]  Khanh Dai Pham,et al.  Statistical Control Paradigms for Structural Vibration Supression , 2004 .

[12]  Sulema Aranda,et al.  On Optimal Sensor Placement and Motion Coordination for Target Tracking , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

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

[14]  Jacob Engwerda,et al.  LQ Dynamic Optimization and Differential Games , 2005 .

[15]  Khanh Pham,et al.  Autonomous Observability of Networked Multisatellite Systems , 2009 .

[16]  R. Duncan Luce,et al.  Several possible measures of risk , 1980 .

[17]  Cédric Langbort,et al.  Distributed control design for systems interconnected over an arbitrary graph , 2004, IEEE Transactions on Automatic Control.

[18]  Rhodes,et al.  Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games , 1973 .