A nonprobabilistic time-variant reliability-based optimization approach to the reliable active controller design of structural vibration considering convex uncertainties

It is observed that the controller, as the “brain” of the active control system, plays a vital role in the vibration-rejecting aspect, and thereby, techniques of the optimal controller design are attracting increasing attention in dynamical engineering recently. However, due to the existence of uncertainty effects originating from modeling parameters and environmental conditions, current design means based on the classical optimal control theory are no longer feasible. In view of this, a new nonprobabilistic time-variant reliability-based optimization (NTRBO) strategy considering convex uncertainties is presented in this study for the reliable controller design of structural vibration. Boundary rules and autocorrelation characteristics of dynamical responses under the linear quadratic regulator control are first determined using the state-space transformation and the convex process theory. Inspired by the out-crossing idea and the safety factor notation, a new piecewise function of the time-variant reliability index is defined, and the nonprobabilistic reliability constraint is then established. Weighing matrices in the Riccati equation, as the keys to construct the controller, are indeed optimized by solving the developed NTRBO model. The usage, validity, and efficiency of the presented reliable control methodology are eventually demonstrated by several example applications.