Discounted cost infinite time horizon cumulant control

Cumulants are gaining in popularity for use in stochastic control and game theory. They also have been effective in application to building and vibration control problems. Much of the work has been done for the finite time horizon case. In this paper, cost cumulants will be used on a discounted cost function. The control will be concerned with the first two cumulants, the mean and variance. The approach will initially be done for a nonlinear system with non-quadratic costs and sufficient conditions are determined. With the sufficient conditions in place, attention will be turned to the linear quadratic special case. A coupled Riccati equation will be seen to give an optimal cumulant control law.