ADP-Based Model Reference Adaptive Control Design for Unknown Discrete-Time Nonlinear Systems

In engineering applications, it is very useful to make a nonlinear system behave like a linear stable system. However, how to design a model reference adaptive control (MRAC) as the nonlinear dynamics is unknown is the key problem. In this study, an MRAC with adaptive dynamic programming (ADP) algorithm is presented for discrete-time nonlinear unknown dynamic systems, in which a multi-layer neural network (NN) model is utilized to describe the nonlinear system's dynamics. Then based on this approximate model, a feedforward neuro-controller is developed as the desired control corresponding to the reference input. Third, the iterative ADP algorithm, in the form of actor-critic framework, employs two NNs to estimate the action value function, and generates the feedback control which, together with the feedforward neuro-controller, makes the state of the system track the reference model. Finally the feasibility of the new approach is verified by two numerical experiments.