Model-free periodic adaptive control for a class of SISO nonlinear discrete-time systems

Using the known periodicity of the given trajectory, we develop a new dynamical linearization method by introducing a concept of PPD, then present a new model-free periodic adaptive control approach (MFPAC) and its extension of higher-order learning control algorithm for a class of general nonlinear and non-affine discrete-time systems. It is model-free in nature and the controller design and analysis only depends on the I/O data of the dynamical system. The proposed MFPAC updates the PPD estimate values and the control signals periodically in a pointwise manner using the I/O data obtained at the corresponding points in previous periods, in the sequel achieves an asymptotic tracking convergence. A simulation example illustrates the feasibility and effectiveness of the proposed method.