Keywords: reliability based design, multiple model active controller, vibration control.

In the field of vibration control, the linear-quadratic-Gaussian (LQG) based techniques have been widely used in recent decades. However, such a kind of controller can barely be applied when considering time-varying parameters and broadband excitations. Moreover, the uncertainties of parameters challenge the running reliability. Some efforts have been undertaken to develop adaptive control schemes, As far as we know, however, there are few publications that discuss the reliability analysis of adaptive controllers for nonlinear stochastic vibration.

The scope of this paper is to tackle the uncertainties of the vibration system while considering the dynamic reliability at the same time. The main contribution is that a reliability-constrained multiple model adaptive (MMA) controller is proposed to reduce vibration in structures, and the reliability of the overall output of a multiple model system is also estimated. The basic idea is to consider that most of structural and mechanical vibration processes can be treated as a piecewise linear-time-invariant (LTI) process. Like conventional techniques, each of LTI subsystem is controlled by one linear-quadratic-Gaussian (LQG) design. A continuous-time based probability updating process is used to interpret Markov jumping among the models which control the blending coefficients of individual optimal controllers. The sole failure mode considered is the first-passage (FP) of the vibration response over an allowable value. To control above a certain reliability level in each individual controller, the first-passage based reliability constraint and cost index are both taken into account as functions of feedback gain and second-moment state statistics. These statistics come from the Lyapunov equation solution, which is so implicit for the reliability calculation that the optimization is no more a LQG problem. Hence, a gradient based genetic algorithm is employed to perform the global feedback gain optimization. Thereafter, the output reliability of the proposed controller is analyzed by integrating the vibration covariance. From the simple case of a two degree-of-freedom structure, numerical examples and comparative results illustrate the differences between reliability-unconstrained problems and their reliability-constrained equivalents. It is concluded that multiple model adaptive controller outperforms single model controller for vibration control in the case of uncertain parameters and excitations. A reliable multiple model system can be created by means of reliability constraints and the reliability requirement of the overall system can be easily satisfied. In the sense of first-passage failure, reliability constraints result in a much more reliable controller without significant loss of performance.

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