Third cumulant statistical control of the first generation structural benchmark problem

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 three cumulants, the mean, variance, and skewness. A coupled Riccati equation is given with an optimal cumulant control law. The results are applied to a three story building subject to a seismic disturbance and those results are compared with other cumulant controllers, including the well-known LQG control method.