Model-Free Adaptive Control for a Class of Nonlinear Discrete-Time Systems Based on the Partial Form Linearization

Abstract

The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in the neighborhood of the equilibrium state. However, it is inconvenient for purposes of adaptive control due to its nonlinear dependence on the control input, even by using the neural network method. In this paper, we introduce a so called model-free adaptive control (MFAC) method, which is based on some new dynamical linearization model and concept, the partial form linearization (PFL) and the pseudo-partial derivative (PPD) of a SISO nonlinear discrete-time system. The model-free means that the controller design is only based on the I/O data of the controlled plant, no training process, no structure information and no model are needed. Rigorous analysis and extensive simulations have shown that it has BIBO stability and performs very well.