Self-Tuning Methods for Multiple-Controller Systems

The optimization of stochastic systems with unknown parameters and multiple decision-makers or controllers each having his own objective is considered. Based on a centralized information pattern, a steady-state solution is obtained for the stochastic adaptive Nash game problem. This adaptive solution, after a judicious transformation, resembles closely the implicit self-tuning solution for the single-controller single-objective case, and thus preserves the salient and advantageous features of self-tuning methods-simplicity and ease of implementation. In addition, due to this close resemblance, convergence for the game problem is established by extending the convergence result from the single-controller single-objective case. In the course of solving the Nash game problem, the extension of the single-input single-output self-tuning controller (STC) to the multiple-input multiple-output (MIMO) case is accomplished and the convergence of the MIMO STC is established. Simulation results of a simplified economic system are presented to illustrate the proposed adaptive game method.