# State-of-the-Art Review of Structural Vibration Control: Overview and Research Gaps
## 6 Optimized Control System Designed to Tackle Practical Implementation Challenges
### Control Systems to Ensure Robustness to Uncertainties  
This review observes that most control algorithms developed are investigated for their robustness and stability in response to system uncertainties, such as stiffness and mass. Conventional control algorithms rely on nominal models and may not work well in uncertain models [42]. Various methods, including \(\mathrm{H_{\infty}}\), \(\mathrm{H_{2}}\), \(\mathrm{H_{\infty}}/\mathrm{H_{2}}\), \(\mathrm{\mu}\)-synthesis, and linear matrix inequalities, are employed for robust controller design. Table 4 presents a comprehensive overview of advanced control algorithms specifically designed to address various types of uncertainties commonly encountered in structural systems. These uncertainties may include variations in structural damping, changes in frequency content due to ground motion characteristics, the nonlinear behavior of materials and components, and inherent time delays in sensing, computation, and actuation. To manage these complex and dynamic challenges, the following table highlights several sophisticated control strategies that have shown promising results in both theoretical and experimental studies. Among these, the Discrete Wavelet Transform (DWT) stands out for its ability to decompose non-stationary signals and extract relevant features in both time and frequency domains, making it suitable for real-time monitoring and adaptive control during seismic events. Fuzzy logic control is another method, known for its effectiveness in handling imprecise or ambiguous input data. This approach does not require a precise \begin{table}
\begin{tabular}{c c c} \hline \hline
**Publication** & **Method Used** & **Issues Addressed** \\ \hline \multirow{3}{*}{([PERSON] and [PERSON]) [184]} & Discrete Wavelet & \multirow{3}{*}{Uncertainty in structural damping and earthquake} \\  & Transform and particle swarm optimization & \\ \hline \multirow{3}{*}{([PERSON] and [PERSON]) [185]} & Wavelet analysis and pattern search method & \multirow{3}{*}{Uncertainty in the frequency content of earthquakes} \\  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \hline ([PERSON] et al.) [186], ([PERSON] and [PERSON]) [187] & Fuzzy logic-based control & \multirow{3}{*}{Nonlinearity} \\  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \hline \multirow{3}{*}{([PERSON] et al.) [189]} & New fuzzy sliding mode & \multirow{3}{*}{Uncertainty and time delay} \\  & controller & & \\ \cline{1-1}  & Adaptive neuro-fuzzy & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \hline ([PERSON] and [PERSON]) [190] & Adaptive block & \multirow{3}{*}{Unknown parameters} \\  & & backstepping & \\ \hline ([PERSON] et al.) [104] & Fuzzy type-1 and type-2 & \multirow{3}{*}{Uncertainties} \\ \hline \multirow{3}{*}{([PERSON] et al.) [191]} & Model reference adaptive & \multirow{3}{*}{\begin{tabular}{} \end{tabular} } & \multirow{3}{*}{\begin{tabular}{} \end{tabular} } \\  & backstepping control & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \hline \multirow{3}{*}{(Zabihi-Samani and Ghanooni-Bagha) [101]} & Adjustable cuckoo search & \multirow{3}{*}{\begin{tabular}{} \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{} \end{tabular} } \\  & Wavelet-based fuzzy logic & \\ \cline{1-1}  & controller (ACSWBFLC) & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & \\ \hline ([PERSON] et al.) [170] & Fuzzy-LQR Algorithm & \multirow{3}{*}{
\begin{tabular}{} \end{tabular} } \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Robust control algorithms for uncertainties. mathematical model of the system; instead, it relies on rule-based reasoning, making it particularly suitable for systems that are uncertain or nonlinear in nature. Additionally, Adaptive Neuro-Fuzzy Inference Systems (ANFISs) are employed as a hybrid method, combining the learning capabilities of neural networks with the interpretability of fuzzy logic.