# State-of-the-Art Review of Structural Vibration Control: Overview and Research Gaps
## 5 Control Algorithms Used for Different Semi-Active Control Systems
### Classification of Control Algorithms
These uncertainties--arising from external excitations or inaccuracies in structural response measurements--can degrade control system performance. Robust control addresses these challenges during the design phase to maintain reliable operation. Among the prominent methods are the H\({}_{\infty}\) and H\({}_{2}\) controllers. The H\({}_{\infty}\) controller uses a combination of time- and frequency-domain approaches to tackle a wide range of control problems. It excels in disturbance rejection and guarantees system stability under diverse operating conditions [165]. Its popularity stems from its flexibility--performance goals can be incorporated as weighting functions during the design process. The H\({}_{\infty}\) framework also includes process and measurement noise, making it robust to model uncertainties. It is suitable for both single-input single-output (SISO) and multi-input multi-output (MIMO) systems. The H\({}_{2}\) controller is a specific subset of the H\({}_{\infty}\) approach. It minimizes the H\({}_{2}\) norm, aiming for optimal performance while stabilizing the system. Like H\({}_{\infty}\), the H\({}_{2}\) controller typically follows a two-input, two-output configuration and is particularly effective for systems where the emphasis is on minimizing overall energy or variance in the output. Robust control is favored for its ability to function without a structural model and handle system uncertainties, but its complex design poses practical challenges. One of the limitations of a robust control system is that time-domain constraints cannot be integrated easily. Adaptive control algorithms are designed to respond to changes, uncertainties, and the random nature of control systems, whether in the controller itself or the feedback and feedforward signals. In recent years, adaptive control strategies have been widely explored both numerically and experimentally in the field of structural control for various civil engineering applications [166; 167; 168]. Adaptive control demonstrates strong real-time adaptability and robustness under both linear and nonlinear conditions by dynamically responding to uncertainties, albeit at the cost of increased design complexity. This comparison underscores the importance of selecting control algorithms based on specific structural needs, performance criteria, and implementation feasibility [169]. Figure 3: Classification of control strategies based on the type of input. The accuracy of nonlinear system modeling has a significant impact on the effectiveness of traditional control algorithms. While conventional control strategies account for uncertainties in measuring both input excitations and system responses, their success still largely depends on the specific control law used. In contrast, intelligent control systems enhance these algorithms by incorporating elements such as reasoning, computation, and decision-making, while also addressing uncertainties in system identification and modeling. This makes intelligent controls a more realistic approach, offering a wider range of solutions. Intelligent systems are influenced by human input, which introduces the potential for error due to reliance on the designer's experience. Intelligent control methods are typically classified into three main types: (a) fuzzy control, (b) neural network control, and (c) genetic algorithms. Neural network control and fuzzy logic control both eliminate the need for predefined structural models, relying instead on data-driven or rule-based approaches [122, 170, 171, 172, 173]. While they offer flexibility for nonlinear systems, they face challenges related to training complexity, stability, and design intricacy. These algorithms  
Figure 4: Classification of control algorithms based on different factors. do not consider feedback from the actuator and rely solely on the structural responses, which can be difficult to obtain during seismic events.