Decentralized H PID Team Formation Tracking Control of Large-Scale Quadrotor UAVs Under External Disturbance and Vortex Coupling

Abstract

For more practical applications, a simple decentralized <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> proportional-integral-derivative (PID) team formation tracking strategy is proposed in this study for large-scale stochastic quadrotor unmanned aerial vehicles (UAVs) under external disturbance, intrinsic stochastic fluctuation and trailing vortex coupling. By adopting the virtual leader concept, the reference trajectory of each UAV is generated by the combination of virtual leader trajectory with a specific time-varying formation offset to form a desired flight formation shape. Then, by using the proposed optimal H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> decentralized PID controller, each UAV can efficiently attenuate the effect of external disturbance and trailing vortex coupling from the neighboring quadrotor UAVs on the team formation reference tracking performance simultaneously. To avoid solving a complex nonlinear Hamiltion Jacobi inequality (HJI) for PID control of each UAV, the Takagi-Sugeno (T-S) fuzzy method is employed to interpolate several local linearized UAVs to approximate the nonlinear stochastic quadrotor UAV system so that the HJI can be transformed to a set of bilinear matrix inequalities (BMIs). By using novel variable transformation method, the optimal decentralized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> PID team formation tracking control problem of large-scale UAVs can be independently designed in terms of a set of independent LMIs-constrained optimization problems for each quadrotor UAV. Further, to simplify the design procedure in a single run, the large amount of decentralized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> PID controller parameters for each quadrotor UAV in the team formation can be efficiently obtained via the current convex optimization technique without any conventional parameter tuning procedure for PID design. Finally, a simulation example of team formation reference tracking control for 25 quadrotor UAVs with external disturbance and vortex coupling is given to validate the team formation tracking performance of the proposed decentralized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> PID tracking control method in comparison with conventional decentralized <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> T-S fuzzy tracking control scheme.