Generalization of Optimal Control Theory: Linear and Nonlinear Control

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Abstract
A generalization of the linear quadratic regulator control theory for seismic‐excited linear structures is presented. The generalization includes the effect of actuator dynamics and a penalty for the acceleration response of the structure. A nonlinear control method is also proposed for nonlinear or hysteretic structural systems with emphasis placed on the applications to aseismic hybrid control systems. In protecting nonstructural components housed in the building against strong earthquakes, the reduction of the building acceleration response is important. The adverse effect of a system time delay due to the actuator response can be alleviated by taking into account the actuator dynamics in the optimization process. Simulation results are presented to demonstrate the advantages of generalized optimal control. Numerical results further indicate that the performance of the proposed nonlinear control method is better than that of the linear control law for hybrid control systems.

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