## 4 Application of Control Parameter Optimization on Five-Story Benchmark Structure
As communication overhead is a common challenge associated with WSUs and in particular when applied to control applications, an additional cost function,  
\[J_{6}=\frac{NP_{1}}{NP_{2}}, \tag{17}\]  
is introduced that compares the amount of data that is transmitted during the execution of the weighted-sum control algorithm versus the amount of data that is transmitted during the execution of the traditional LQR algorithm. In this cost index, \(NP_{1}\) is the number of peaks that are detected from all filters across all floors. \(NP_{2}\) is the number of data points obtained via traditional Nyquist sampling rates, combined across all floors. While the weighted-sum method does use asynchronous sampling to generate the number of peaks, the bandpass filters decompose the displacement of each floor into eleven signals that must be transmitted, albeit as peaks, to the controller nodes. For all three earthquakes, this resulted in an undesirable increase in information flow, as indicated by \(J_{6}\) being greater than 1.0 (Tables 3-5). It is hypothesized, however, that not all connections are needed in the weight matrix and some filters can be eliminated from the algorithm. This in turn would reduce the information flow and address one of the common challenges associated with control using WSUs. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Control Scenario**} & \multicolumn{1}{c}{**Floor**} & \multirow{2}{*}{**1**} & \multirow{2}{*}{**2**} & \multirow{2}{*}{**3**} & \multirow{2}{*}{**4**} & \multirow{2}{*}{**5**} \\ \cline{3-3} \cline{5-7} \multicolumn{1}{c}{**Control Scenario**} & & & & & & \\ \hline \multirow{3}{*}{\(J_{1}\)} & Weighted-sum & 0.414 & 0.383 & 0.364 & 0.360 & 0.614 \\  & Weighted-sum-220 & 0.386 & 0.379 & 0.326 & 0.302 & 0.514 \\  & LQR & **0.286** & **0.226** & **0.204** & **0.213** & **0.222** \\ \hline \multirow{3}{*}{\(J_{2}\)} & Weighted-sum & 0.468 & 0.449 & 0.446 & 0.490 & 0.613 \\  & Weighted-sum-220 & 0.454 & 0.439 & 0.421 & 0.456 & 0.514 \\  & LQR & **0.241** & **0.201** & **0.191** & **0.189** & **0.187** \\ \hline \multirow{3}{*}{\(J_{3}\)} & Weighted-sum & 1.030 & 0.465 & 0.579 & 0.671 & 0.696 \\  & Weighted-sum-220 & 1.252 & 0.463 & 0.597 & 0.637 & 0.601 \\  & LQR & **0.459** & **0.366** & **0.423** & **0.399** & **0.367** \\ \hline \multirow{3}{*}{\(J_{4}\)} & Weighted-sum & 0.975 & 0.631 & 0.593 & 0.519 & 0.492 \\  & Weighted-sum-220 & 0.873 & 0.621 & 0.573 & 0.496 & 0.443 \\  & LQR & **0.395** & **0.327** & **0.295** & **0.273** & **0.257** \\ \hline \multirow{3}{*}{\(J_{5}\)} & Weighted-sum & 0.123 & 0.129 & 0.143 & **0.161** & 0.477 \\  & Weighted-sum-220 & 0.154 & 0.225 & 0.179 & 0.295 & 0.400 \\  & LQR & **0.060** & **0.094** & **0.141** & 0.179 & **0.222** \\ \hline \multirow{3}{*}{\(J_{6}\)} & Weighted-sum: LQR & \multirow{3}{*}{} & \multirow{3}{*}{} & \multirow{3}{*}{} & \multirow{3}{*}{} \\  & Weighted-sum-220: & & & & & \\ \cline{1-1}  & LQR & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Cost functions \(J_{1}\) through \(J_{6}\) for Loma Prieta earthquake. Bold indicates the cost function that yields the minimum cost function for each floor.