Stochastic Differential Games with Complexity Constrained Strategies.

摘要

An examination is made of some problems encountered in the optimal control of a linear dynamic system by two independent controllers with noisy state observations, the controllers having either conflicting or concurring objectives. The question of what form the optimal controls should take is also discussed. By restricting consideration to linear forms, it is shown that the computational complexity of a general optimal linear strategy is considerable. Attention is further restricted to a particular linear form for the optimal controls: a matrix transformation of a vector which is the solution of a linear differential equation forced by the observations. Properties of certain forms of this type of control are analyzed, and it is shown that the parameters of these forms may be expressed in terms of solutions to a set of nonlinear differential equations with split boundary conditions. It is also demonstrated that these forms reduce, in a one-input case, to those specified by the separation principle of one-sided optimal control. (Author)