Multi-cumulant, multi-objective structural control: a circuit analog

Abstract

Cost cumulant control has been gaining momentum in recent years and has proven to be competitive with other controllers when applied to various structural control problems. These control methods have generalized the well-known LQG control. Similarly, in this paper cost cumulants are used to generalize the H 2 =H 1 control problem. Initially the development will be done for a class of nonlinear systems. The treatment will then consider the case when the system is linear and the costs are quadratic. The multi-cumulant, multiobjective control strategy, as well as the worst case disturbance, will be found through a Nash game approach. Uncertainties in the stiffness and damping coefficients will be taken into account and this control strategy will be applied to a four story building subject to a seismic disturbance. Also, a connection of the building problem to circuits will be given.

Multiplayer nash solution for noncooperative cost density-shaping games

“…In [4], a four-story structure is considered. A cost densityshaping game will be posed using this system, which has two disturbances -the ground excitation, and also uncertainties in the system.…”

“…For the case of linear controls and integral-quadratic cost functionals, kCC control theory is the foundation for the study of kCC zero-sum and Nash games [1]. For the more general case of nonlinear controls and integral non-quadratic cost functionals, the cost cumulant games theory has been developed, again in the non-cooperative setting [4]. This work has in fact generalized the classical H 2 /H ∞ theory and strengthened the connection between cost cumulant control and robust control theories.…”