Reliable Model Predictive Vibration Control for Structures with Nonprobabilistic Uncertainties

Abstract

This paper proposes a novel reliable model predictive control (MPC) method for active vibration control of structure with nonprobabilistic uncertainties. First, the framework of reliable MPC is established by integrating nonprobabilistic reliability constraints into nominal MPC. Based on the first‐order Taylor expansion and first‐passage theory, an efficient nonprobabilistic reliability analysis method that is suitable for online computation is proposed. A nonprobabilistic Kalman filter is further proposed for determine system states and their uncertain region. Unlike most robust MPC approaches, the proposed reliable MPC focuses on the satisfaction of state constraints in terms of structural reliability and is more suitable for structures with stringent safety requirements. Compared to existing reliability‐based vibration control methods, reliable MPC requires no knowledge of disturbance and exhibits greater adaptability to load environments. The effectiveness and superiority of the proposed reliable MPC are validated through a numerical example and an engineering case study.