Compact Model-Free Adaptive Control Algorithm for Discrete-Time Nonlinear Systems

In model free adaptive control (MFAC), a virtual equivalent dynamic linearized model is built. The linearization length constants (LLCs) of the virtual equivalent dynamic linearized model are selected by the practitioner based on experience. In this paper, the optimal LLCs are investigated, and compact model free adaptive control (CMFAC) is introduced for a class of unknown discrete-time nonlinear systems. Compared with MFAC, the proposed CMFAC does not need to consider the values of LLCs, and the optimal LLCs are decided by the desired tracking error of systems. Simulation experiments are taken, and the simulation results indicate that the proposed control algorithm is effective and can achieve asymptotic tracking.