Data-Driven Tracking for Nonlinear Systems: A Multi-Step Error Feedback Model-Free Adaptive Control Method

A multi-step error feedback model free adaptive control (MSEF-MFAC) method is proposed for the trajectory tracking problem of discrete nonlinear systems with unknown dynamics. To improve the utilization of historical tracking error information, the implemented control protocol incorporates the concept of multi-step error feedback using a vector data transmission mechanism, encompassing the proportional control term, the differential control term, and the quadratic difference control term. Furthermore, the theoretical stability of the MSEF-MFAC scheme is demonstrated. Numerical simulations affirm the superior control performance of the MSEF-MFAC scheme, outperforming both the PID scheme and three other Model-Free Adaptive Control (MFAC) methods.