## Appendix A Proof of Theorem 1
Combining (10) and (39a), it yields:\[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]0 \[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]1 \[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]2 \[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]3 \[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]4 \[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]5 \[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]6  
where \(\alpha_{v2i}=\min\{||\Phi_{f}||^{2}\frac{\xi_{i}}{\xi_{fi}^{2}},2\gamma_{s}g _{is}k_{1i}^{s},2\gamma_{f}k_{1i}^{f}\}\), \(\beta_{v2i}=2\gamma_{s}g_{is}k_{3i}^{s}\kappa_{0}e_{s}+2\gamma_{f}k_{3i}^{f} \kappa_{0}e_{f}\). Noting \(|\tilde{\psi}_{fi}|>\overline{\xi}_{fi}\), \(\overline{\xi}_{fi}\geq|\xi_{fi}|\). It is clear that \(\dot{V}_{oi}<0\) is true as long as \(V>\frac{\beta_{v2i}}{\alpha_{v2i}}\). Case 1c: When \(|\tilde{\psi}_{fi}|\leq\overline{\xi}_{fi}\) & \(\Phi_{f}^{T}F_{i}\Phi_{f}\leq\overline{\xi}_{fi}^{2}\) hold, that is, \(b_{i}=0\) in this case, which implies \(\dot{V}_{i}=0\). Combining (10) and (39a), one obtains:  
\[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]7 \[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]8 \[\dot{V}_{oi}\!=\!2\gamma_{s}s_{is}s_{is}\!-\!2\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{ W}_{i}\!+\!\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!+\!\frac{2\gamma_{f}s_{if} ds_{if}}{dt_{\epsilon}}.\]9 \[\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!\geq\!\hat{W}_{i}^{T}F_{\,i}^{-1} \Bigg{(}\frac{\xi_{i}}{\xi_{fi}^{2}}b_{i}F_{\,i}\Phi_{f}\vec{\psi}_{fi}\!+\! \gamma_{s}s_{is}F_{\,i}\Phi s_{is}\!-\!\gamma_{f}K_{0}F_{\,i}\Phi s_{if}\Bigg{)}.\]0 \[\hat{W}_{i}^{T}F_{\,i}^{-1}\hat{W}_{i}\!\geq\!\hat{W}_{i}^{T}F_{\,i}^{-1} \Bigg{(}\frac{\xi_{i}}{\xi_{fi}^{2}}b_{i}F_{\,i}\Phi_{f}\vec{\psi}_{fi}\!+\! \gamma_{s}s_{is}F_{\,i}\Phi s_{is}\!-\!\gamma_{f}K_{0}F_{\,i}\Phi s_{if}\Bigg{)}.\]1  
where \(\alpha_{v3i}=\min\{2\gamma_{s}g_{is}k_{1i}^{s},2\gamma_{f}k_{1i}^{f}\}\), \(\beta_{v3i}=2\gamma_{s}g_{is}k_{3i}^{s}\kappa_{0}e_{s}+2\gamma_{f}k_{3i}^{f} \kappa_{0}e_{f}\). It is clear that \(\dot{V}_{oi}<0\) is true as long as \(V>\frac{\beta_{v3i}}{\alpha_{v3i}}\). Combining the above analysis in cases 1a-1c, it can be concluded that \(\hat{W}_{i}(t)\in\Omega_{E_{i}},\forall t\geq 0\) if \(\hat{W}_{i}(0)\in\Omega_{E_{i}}\). **Step 2**, the boundedness of the identification error \(\tilde{\psi}_{fi}\) is proved.