International Journal of Electrical and Computer Engineering (IJECE) Vol. 12, No. 4, August 2022, pp. 3607~3619 ISSN: 2088-8708, DOI: 10.11591/ijece.v12i4.pp3607-3619  3607 Journal homepage: http://ijece.iaescore.com Adaptive proportional integral derivative deep feedforward network for quadrotor trajectory-tracking flight control El Ayachi Chater 1 , Halima Housny 2 , Hassan El Fadil 2 1 LASTIMI Laboratory, Higher School of Technology, Mohammed V University, Rabat, Morocco 2 ISA Laboratory, National School of Applied Sciences, Ibn Tofail University, Kenitra, Morocco Article Info ABSTRACT Article history: Received Apr 29, 2021 Revised Mar 21, 2022 Accepted Apr 2, 2022 When the controlled system is subject to parameter variations and external disturbances, a fixed-parameter proportional integral derivative (PID) controller cannot ensure its stabilization. In this case, its control requires online parameter adjustment. Specifically, as the quadrotor is a multi-input multi-output, nonlinear, and underactuated system, robust control is necessary to ensure efficient trajectory tracking flights. In this paper, an adaptive proportional integral derivative (APID) controller is proposed to control the quadrotor systems. This APID-based control strategy uses a two hidden layer deep feedforward network (DFN), where the one-step secant algorithm is chosen for initializing the DFN parameters. All the design steps of the proposed adaptive controller are described. The multidimensional particle swarm optimization (PSO) algorithm is used for tuning the DFN parameters. Then, using two simulation efficiency tests, a comparison between the proposed PSO-based APID-DFN, the (non-optimized) APID-DFN, the feedforward network APID, and the fixed-parameter PID controllers proves much efficiency of the proposed adaptive controller. The results illustrate that the proposed PSO-based APID-DFN controller can ensure good quadrotor system stabilization and achieve minimum overshoot and faster convergence speed for all quadrotor motions. Thus, the proposed control strategy could be considered an additional intelligent method-based adaptive control for unmanned aerial vehicles. Keywords: Adaptive proportional integral derivative Deep neural network Feedforward network Multidimensional particle swarm optimization Quadrotor system This is an open access article under the CC BY-SA license. Corresponding Author: El Ayachi Chater LASTIMI Lab., Higher School of Technology, Mohammed V University Rabat, Morocco Email: elayachi.chater@est.um5.ac.ma 1. INTRODUCTION Over the last years, the research control community has shown an increasing interest in flying vehicles without onboard human pilots known as unmanned aerial vehicles (UAVs). UAVs’ civilian applications have increased in diverse fields due to their low cost. Their application ranges from homeland security, disaster relief, and weather forecasting to power line inspection and precision agriculture [1]–[3]. Besides, as in the outdoors environment, the aerial vehicles are exposed to adverse atmospheric conditions, reliable and robust control strategies are necessary. Many papers deal with the control problem of the multi-rotor UAV systems. Some of these works propose the development of linear controllers like the proportional integral derivative (PID) and linear-quadratic regulators (LQR) [4], [5]. Besides, other works suggest the development of nonlinear methods to ensure UAV system stability. Among the latter, we can list the backstepping control approach [6], [7] and the sliding mode approaches [8], [9]. In addition, intelligent control strategies have been vastly used