Multiplayer nash solution for noncooperative cost density-shaping games

Finite-horizon, LQ cost density-shaping has been achieved through several different control paradigms that are based on the Multiple-Cumulant Cost Density-Shaping (MCCDS) theory. With these cost density-shaping control methods, the shape of a target cost density can be transformed into a linear control law. However, the existing MCCDS theory does not permit control design that accounts for competing objectives among multiple noncooperative agents. The aim of this work is to derive the Nash equilibrium solution to an N-Player MCCDS game posed for the LQG framework. Simulation results are provided to support the new theory.