Robust Control for Structural Systems with Unstructured Uncertainties

Natural hazards, such as earthquakes and strong wind events, place large forces on tall, slender structures and on long-span bridges. In view of the numerous uncertainties due to model errors, stress calculations, material properties, and environmental loads, the structural system is uncertain. Here, the Lagrangian representation is modeled as an uncertain state-space model. The paper develops a robust active control approach with uncertainties in not only the system and control input matrices, but also the disturbance input matrices. Robust active control provides both robust relative stability and $H_{\infty }$ disturbance attenuation. The $H_{\infty }$ norm of the transfer function from the external disturbance forces (e.g., earthquake, wind, etc.) to the observed system states is restricted by a prescribed attenuation index. The uncertainties considered herein are norm-bounded unstructured uncertainties. Preservation of $H_2$ optimality of robust structural control is also revealed. The results may be further extended to structured uncertainties. A numerical example illustrates that the approach may be applied to robust control of structural systems under earthquake excitation.