An evolutionary gain formulation is proposed for minimizing the performance damage index of steel buildings subjected to earthquake forces. The gain formulation herein is used to develop the evolutionary control law of a control algorithm applied to inelastic systems. The optimal evolutionary gain is subsequently used to control building damages by satisfying desired performance objectives per time step "as needed". The performance objectives are defined for various "damage-safe" and elastic demands. When the structure responds in the post-yield (inelastic) state, the material is assumed to follow a kinematic rule for strain hardening, which consequently may redefine the performance objective window at each unload/reload response state (cyclic control).A control nonlinear time-history analysis program, dubbed CONON, was developed to simulate the stress-strain responses of structural members and to compute the optimal control forces per time step. The minimization of the cost function is independent of weighing matrices, thus alleviating cumbersome calculations that also lack physical description. Instead, an iterative Riccati matrix is computed per time step and is used to generate the evolutionary gain for the system leading to an appropriate evolution of the state transition between time steps. The calculated control responses are compared to uncontrolled responses. The results are also compared using various methods of gain calculation by examining the force-deflection hysteresis plots, the strain energy dissipation in the structural members, and the member accelerations of a steel frame. The proposed optimal system shows an excellent capability to control the desired target responses and meet acceptable performance objectives.

An evolutionary gain formulation is implemented within a nonlinear quadratic control algorithm framework used to minimize the performance index of a structural steel system that is subjected to various earthquake ground motions. The control architecture is formulated using a numerical integration scheme that solves the nonlinear responses of a degrading system and formulates an optimal gain matrix that is used to control building displacement demands by satisfying the desired performance-objectives per time-step. The performance-objectives are defined for various 'damage-safe' and elastic demands to show the versatility of the proposed control solution. The results of the evolutionary gain approach are compared to more conventional LQR techniques. Towards this end, a COntrol NONlinear time-history analysis (CONON) program was developed to simulate the responses of kinematically strain-hardened systems and to compute the optimal semi-active device output forces per time-step as part of the control solution that implements the proposed evolutionary gain. The minimization of the cost function is independent of the weighing matrices of the system, thus alleviating any need to compute these terms per time step. Instead, an iterative Riccati matrix is determined per time-step and used to generate the evolutionary gain. The results are compared by examining several hysteresis plots of the steel system against other feedback-based methods. The proposed system implementation shows a marked increase in the ability to control the desired target response and meet acceptable performance goals.