A sampled data equilibrium Stackelberg coordination scheme for the multicontroller problem

Abstract

In this paper we consider a multicontroller problem in which each control agent has a different objective function. The actions of the controllers are coordinated by the influence of one controller who plays according to a Stackelberg strategy relative to the remaining players. We investigate this formulation when the information flow is restricted by constraining it to be in the form of sampled data acquisition. The computational advantage of the sampled data formulation is quite significant. Of equal importance is the relationship among the sampled data, closed-loop, and open-loop problems. The existence of and solution for the closed-loop Stackelberg solution for the continuous-time game are, at present, unresolved problems. The primary motivation for considering the sampled data formulation is to obtain a solution which maintains the computational simplicity of the tractable open-loop solution while gaining the responsiveness of a state feedback solution, avoiding the complications of the purely closed-loop formulation. The linear quadratic problem is considered in detail, and an efficient solution algorithm is derived which takes advantage of certain characteristics of the sampled data solution.