Pricing design for robustness in linear quadratic games

We show that designing prices to induce a socially optimal Nash equilibrium that is robust to small parameter perturbations in a linear-quadratic game can be framed as a convex program. In addition, we use a similar analysis to develop convex conditions that guarantee that the induced equilibrium is stable with respect to small deviations in players' feedback strategies.

[1]  Francisco Rodríguez,et al.  Multiobjective hierarchical control architecture for greenhouse crop growth , 2012, Autom..

[2]  S. Shankar Sastry,et al.  Pricing in linear-quadratic dynamic games , 2012, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[3]  Kaare Brandt Petersen,et al.  The Matrix Cookbook , 2006 .

[4]  Conversion and delivery of electrical energy in the 21st century , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

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

[6]  Pedro Antmann,et al.  Reducing Technical and Non-Technical Losses in the Power Sector , 2009 .

[7]  Tamer Basar,et al.  Distributed algorithms for the computation of noncooperative equilibria , 1987, Autom..

[8]  J. Ortega.  Numerical Analysis: A Second Course , 1974 .

[9]  Thomas B. Smith,et al.  Electricity theft: a comparative analysis , 2004 .

[10]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[11]  Alberto Bressan,et al.  ON THE STABILITY OF THE BEST REPLY MAP FOR NONCOOPERATIVE DIFFERENTIAL GAMES , 2012 .

[12]  John M. Lee.  Introduction to Smooth Manifolds , 2002 .

[13]  F.M. Cleveland,et al.  Cyber security issues for Advanced Metering Infrasttructure (AMI) , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[14]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[15]  Petko H. Petkov,et al.  Perturbation bounds for coupled matrix Riccati equations , 2003 .