This paper formulates and solves an inverse optimal gain assignment control problem for the evolution systems perturbed by unknown (bounded) disturbances in Hilbert spaces. The control design ensures global well-posedness and global (practical), K-infinity,-exponential (respectively, strong or weak asymptotic) stability of the closed-loop system, minimizes a cost functional that appropriately penalizes state, control, and disturbances in the sense that a cost functional, which is positive definite in state and control, and is negative definite in disturbances, is minimized. Thus, the proposed control law minimizes both state and control while attenuates the disturbances. Moreover, it is not required to solve a Hamilton-Jaccobi-Isaacs equation (HJIE) but the Lyapunov functional used in the control design is exactly the solution of a family of HJIEs. The developed results are illustrated via an application to design new inverse optimal gain assignment boundary control laws for mitigating vibration of extensible marine risers under either a positive or zero or even negative pretension subject to sea loads. This optimal control problem for marine risers has not been addressed in the literature. (C) 2019 Elsevier Ltd. All rights reserved.