Discrete-Time Embedded Model Control Scheme for Disturbed Nonlinear Systems With Application to Quadrotor UAVs

In this paper, a discrete-time embedded model control (EMC) scheme is proposed for a class of disturbed nonlinear systems under model uncertainty. First, by invoking the current state, a linear discrete-time embedded model (EM) is real-timely generated by linearizing and discretizing nominal model of nonlinear system. Then, as for the reference dynamics for our control scheme, a reference generator is designed to generate a group of reference control input and reference state. Meanwhile, as for control dynamics for proposed scheme, an auxiliary system and a predictor are combined to compensate for the error of control input. Based on above, a synthetic controller is derived to stabilize the controlled system by combining the reference dynamics and control dynamics. Thus, the discrete-time Lyapunov stability theory is utilized to analyze the overall closed-loop system, and a sufficient stability condition is proposed to guarantee that all the closed-loop states under the proposed EMC scheme are semi-globally ultimately uniformly bounded (UUB), ensuring the ultimate error bounds to be adjusted into tolerable regions. Finally, as for the nonlinear system of quadrotor UAV, some simulations are conducted to illustrate the effectiveness of the proposed control scheme. Note to Practitioners—The motivation of this paper aims to investigate the control stability issue of a disturbed nonlinear system. Currently, these relevant results proposed in existent paper mainly relied on the complicated continuous-time controllers, which are hard to be implemented in practice. Yet, this paper proposes a control scheme based on a discrete-time embedded model, which can ensure the desired control performance. First, a reference signal generator is designed by generating a linear discrete-time embedded model. Based on this, the control error is compensated by combining an auxiliary system and a predictor. Then, a synthetic controller is derived to stabilize the controlled system. The effectiveness of the overall control scheme is validated using a quadrotor UAV nonlinear system, demonstrating that all signals in the closed-loop system under our control scheme are semi-globally uniformly bounded, and the ultimate error bounds can be adjusted to a tolerable range. In future work, we will investigate the problem on input delay compensation based on the control scheme of this paper.