# Hierarchical Coordinated Predictive Control of Multiagent Systems for Process Industries
## 5 Numerical Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Scenario**} & **IAE** & **ITAE** & **ISE** & **ITSE** & **Power Consumption** \\  & & & & **(kWh)** & **TNC** \\ \hline
1 & \(6.1537\times 10^{3}\) & \(4.4741\times 10^{4}\) & \(2.6870\times 10^{6}\) & \(1.2220\times 10^{7}\) & 12.6512 & 541.1240 \\
2 & \(6.0884\times 10^{3}\) & \(4.3369\times 10^{4}\) & \(2.6843\times 10^{6}\) & \(1.1174\times 10^{7}\) & 14.1211 & 1027.3423 \\
3 & \(6.0023\times 10^{3}\) & \(3.8171\times 10^{4}\) & \(2.6835\times 10^{6}\) & \(1.1146\times 10^{7}\) & 14.1857 & 1025.8815 \\
4 & \(6.0226\times 10^{3}\) & \(3.8554\times 10^{4}\) & \(2.6840\times 10^{6}\) & \(1.1156\times 10^{7}\) & 13.0109 & 531.9966 \\
5 & \(6.0179\times 10^{3}\) & \(3.9006\times 10^{4}\) & \(2.6838\times 10^{6}\) & \(1.1152\times 10^{7}\) & 13.3255 & 686.4957 \\
6 & \(6.0302\times 10^{3}\) & \(4.0529\times 10^{4}\) & \(2.6836\times 10^{6}\) & \(1.1155\times 10^{7}\) & 13.7422 & 714.8332 \\
7 & \(6.0704\times 10^{3}\) & \(4.2104\times 10^{4}\) & \(2.6842\times 10^{6}\) & \(1.1169\times 10^{7}\) & 13.2207 & 650.0666 \\
8 & \(6.0877\times 10^{3}\) & \(3.9296\times 10^{4}\) & \(2.6851\times 10^{6}\) & \(1.1188\times 10^{7}\) & 17.3668 & 2375.4160 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: IAE, ITAE, ISE, ITSE values, power consumption and TNC in the 8 scenarios. Figure 6: (a) IEP of each microwave source in scenario 1. (b) Material temperature in scenario 1. Figure 8: (a) IEP of each microwave source in scenario 3. (b) Material temperature in scenario 3. Figure 7: (a) IEP of each microwave source in scenario 2. (b) Material temperature in scenario 2. Figure 9: (a) IEP of each microwave source in scenario 4. (b) Material temperature in scenario 4. Figure 11: (a) IEP of each microwave source in scenario 6. (b) Material temperature in scenario 6. Figure 12: (a) IEP of each microwave source in scenario 7. (b) Material temperature in scenario 7. Figure 10: (a) IEP of each microwave source in scenario 5. (b) Material temperature in scenario 5. The results in Table 4 can provide additional information by considering the characteristics of the four control performance metrics. The values of the IAE and ISE metrics in scenarios 1, 2, 6 and 7 are very close to those of CMPC, which indicates that the proposed HCPC is able to provide dynamic and steady-state performance similar to that of CMPC. However, the relatively poor ITAE metrics and the better ITSE metrics in scenarios 1, 2, 6 and 7 indicate that small deviations from the target occur more frequently in the middle of the control process in these four scenarios and this analysis can be corroborated from the temperature variations in Figures 6b, 7b, 11b, 12b and 13b for the time step \(k\in[25,60]\). The values of the control performance metrics corresponding to scenarios 3, 4 and 5 indicate that the proposed HCPC strategy can provide overall better control performance than CMPC in these three scenarios. Notably, even though the values of the four control performance metrics in the eight scenarios are different, the proposed HCPC can provide very close control performance to that of CMPC, even slightly better than that of CMPC in some cases of systems with decentralized characteristics. From an energy consumption perspective, the corresponding power consumption in scenarios 1-7 is 72.85%, 81.31%, 81.68%, 74.92%, 76.73%, 79.13% and 76.13% of that of scenario 8, respectively. As shown in Figures 6-14 and Table 4, the proposed HCPC can maintain the IEPs of microwave source agents 1, 3 and 5, which have greater heating capabilities, at relatively high levels under different communication topologies while  
Figure 14: Total power consumption for each of the 8 scenarios. Figure 13: (**a**) IEP of each microwave source in scenario 8 (CMPC). (**b**) Material temperature in scenario 8 (CMPC). allowing microwave source agents 2, 4 and 6, which have lower heating capabilities, to play a more auxiliary role.