A Bayesian-Based Credible and Reliable Control Method for Active Vibration Suppression of Structures with Uncertain Parameters

As a classical design method for addressing uncertainty in control systems, robust control is designed with the goal of complete reliability of the control system. Nevertheless, the pursuit of robustness can inadvertently give rise to considerable performance degradation, rendering the resultant closed-loop control system excessively conservative in its design. Reliability-based design methods serve as an effective approach for managing uncertainties, which will achieve a balance between the robustness and performance of the active control system by taking advantage of the characteristic of reliability that allows for a certain level of permissible failure probability. The accurate quantification of uncertainty is the key to achieving reliable control, but common uncertainty quantification methods cannot achieve credible quantification of uncertainty in small samples and update the distribution of new samples. In this paper, a nonprobabilistic Bayesian inference based interval uncertainty quantification method is proposed. This method updates the distribution of interval boundaries and radii by introducing a small number of samples, and obtains interval parameters under a given confidence level. On the basis of uncertainty quantification, the dynamic reliability of the vibration system is derived, and nonprobabilistic reliability is introduced into the design of active controllers through optimization strategies. The reliable control strategy aims to select the optimal controller parameters on a reliable path with a given credibility, in order to solve the problem of overly conservative robust control theory. Two numerical examples were used to verify the feasibility and applicability of this method.