Multi-objective data-driven mixed H2/H∞ controller design for uncertain structural systems

This paper presents a multi-objective, linear matrix inequality-based (LMI-based) data-driven mixed $H_2/H_{\infty }$ control approach for attenuating norm-bounded disturbances in seismically excited structural systems. The identification-free nature of the data-driven control technique effectively addresses parameter uncertainty issues in structural systems. While the proposed technique does not require knowledge of the system matrices $A$ and $B_u$, it only necessitates the bounds on states and disturbances for controller design. In the proposed method, the full-block S-procedure is employed to define the norm-bounded uncertain disturbance input, allowing the use of convex-hull relaxation. Moreover, the dilation technique on LMIs enables the use of non-common Lyapunov matrices in $H_2$ and $H_{\infty }$ control problems. As a result, the proposed method provides a solution to the convex optimization problem for multi-objective control with minimal conservatism. The effectiveness of the proposed data-driven controller is evaluated using a four-storey structural system subjected to ground motions from earthquake data collected during the Kobe and Northridge earthquakes. Numerical examples and extensive case studies demonstrate that the proposed method achieves successful active vibration control comparable to model-based approaches and exhibits robustness under different earthquake excitations and system mass variations.