A multiobjective cost cumulant control problem: the Nash game solution

Recently cost cumulant control has been effectively applied to vibration control problems. Similarly so have multiobjective control paradigms. In this paper the cost cumulant control idea is used to solve the case when the system has some structured uncertainty, with two players, the control and disturbance, having their own performance indices. The development at first is done for a class of nonlinear systems, non-quadratic cost and then is later applied to the linear, quadratic special case. The two performance indices will be linear combinations of cumulants, in which one shall be for the control and the other will constrain the input-output relationship of the disturbance to a output. The control solution is then applied to the First Generation Benchmark for a 3-story building under seismic excitation. The results will be compared with those of several different controllers.