Adaptive MPC Using a Dual Fast Orthogonal Kalman Filter: Application to Quadcopter Altitude Control

This paper presents a novel application of recursive fast orthogonal search (R-FOS) to produce a time-varying linear state-space system model based on a historical record of input and outputs. Themodel is integrated into a larger unmanned aerial system to control the altitude of a quadcopter using adaptive model predictive control (MPC). Similar to a dual Kalman filter (KF), R-FOS is also used in conjunction with a KF observer in the form of a dual fast orthogonal Kalman filter to estimate the system states. Four variations of R-FOS are implemented and compared in terms of mean squared error during a number of simulations. The R-FOS adaptiveMPC strategy provides better altitude control when executed online than when an offline model is used. Comparable performance is achieved with fewer model terms when the FOS criteria for evaluation of additional terms is considered. Finally, the performance is significantly improved when a forgetting factor is incorporated to give greater weight to more recent observations. These findings demonstrate that by combining R-FOS with adaptive MPC, one can optimally control a system with unknown, time-varying dynamics.