# Trajectory Tracking Outer Loop Regressor-Based Adaptive Controller for a Quadrotor
## 5 Conclusions  
In this work, a regressor-based adaptive controller was introduced. The proposed scheme was developed as an outer loop scheme for a quadrotor that has an inaccessible and unmodifiable inner controller. The proposed controller was designed exploiting the structure of the dynamic model of the quadrotor with an inner controller. In addition, an integral action was included to overcome the steady-state error resulting from the parameter estimation error and constant disturbances. The stability analysis of the closed-loop system was presented, guaranteeing the fulfillment of the control goal and assuring the boundedness of the parameter estimation errors. An experimental comparative study regarding a PD scheme and other three neural network-based schemes was presented. The proposed scheme showed competitive performance since similar position and velocity errors compared to the tested controllers were obtained with it.  
Conceptualization, I.L.-S., J.M., L.R.G.C., A.D. and J.M.-V.; methodology, I.L.-S., J.M., L.R.G.C., A.D. and J.M.-V.; software, I.L.-S. and J.M.; validation, L.R.G.C., A.D. and J.M.-V.; formal analysis, I.L.-S. and J.M.-V.; investigation, I.L.-S., J.M., L.R.G.C., A.D. and J.M.-V.; data curation, I.L.-S. and J.M.-V.; writing--review and editing, I.L.-S. and J.M.-V.; visualization, I.L.-S.; supervision, L.R.G.C., A.D. and J.M.-V.; project administration, L.R.G.C., A.D. and J.M.-V.; funding acquisition, J.M.-V. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by Consejo Nacional de Ciencia y Tecnologia, CONACYT-Fondo Sectorial de Investigacion para la Educacion under Project A1-S-24762 and in part by Secretaria de Investigacion y Posgrado-Instituto Politecnico Nacional, Mexico. Proyecto Apoyado por el Fondo Sectorial de Investigacion para la Educacion.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
Conflicts of Interest: The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Signal** & **PDC** & **ANNISMC** & **PI\%** & **GRNNC** & **PI\%** & **ANNC** & **PI\%** & **ARBC** & **PI\%** \\ \hline \(e_{x}\) [m] & 0.0981 & 0.0952 & **2.93** & 0.0480 & 51.11 & 0.0475 & 51.63 & 0.0302 & 69.22 \\ \(e_{y}\) [m] & 0.1104 & 0.0637 & **42.36** & 0.0348 & 68.47 & 0.0330 & 70.12 & 0.0265 & 76.00 \\ \(e_{z}\) [m] & 0.0525 & 0.0256 & 51.29 & 0.0125 & **76.17** & 0.0132 & 74.81 & 0.0386 & **26.47** \\ \(e_{\phi}\) [\({}^{\circ}\)] & 0.9444 & 0.4566 & 51.65 & 0.3426 & 63.72 & 0.4934 & **47.76** & 0.2709 & **71.32** \\ \hline \multicolumn{2}{c}{Average} & \multicolumn{3}{c}{**37.06**} & \multicolumn{3}{c}{**64.87**} & \multicolumn{3}{c}{61.08} & \multicolumn{3}{c}{60.75} \\ \hline \(\dot{e}_{x}\) [m/s] & 0.0654 & 0.0773 & \(-\)**18.23** & 0.0444 & 32.15 & 0.0413 & 36.81 & 0.0243 & 62.90 \\ \(\dot{e}_{y}\) [m/s] & 0.0537 & 0.0413 & **23.14** & 0.0351 & 34.61 & 0.0249 & 53.56 & 0.0164 & 69.38 \\ \(\dot{e}_{z}\) [m/s] & 0.0166 & 0.0384 & \(-\)**132.04** & 0.0257 & \(-\)55.06 & 0.0115 & **30.76** & 0.0219 & \(-\)32.39 \\ \(\dot{e}_{\phi}\) [\({}^{\circ}\)/s] & 1.0723 & 0.7651 & **28.65** & 1.0781 & \(-\)0.55 & 0.8382 & 21.83 & 1.0358 & 3.40 \\ \hline \multicolumn{2}{c}{Average} & \multicolumn{3}{c}{**\(-\)**24.62**} & \multicolumn{3}{c}{2.78} & \multicolumn{3}{c}{**35.74**} & \multicolumn{3}{c}{25.82} \\ \hline \hline \end{tabular}
\end{table}
Table 1: RMS values of \(e(t)\) and \(\dot{e}(t)\) for all the tested controllers.