A New Data-Driven Model-Free Adaptive Control for Discrete-Time Nonlinear Systems

Abstract

The existing model-free adaptive control encounters problems, such as too many parameters that need to be determined, some of which with unclear physical significance and whose selection depend entirely on trial and error. Aiming at this problem, a new dynamic linearized model is established by using Taylor series expansion of discrete-time nonlinear systems and the differential mean value theorem. Then, a new data-driven model-free adaptive control is proposed, which reduces the required parameters from six in the existing model-free adaptive control to four in the new model-free adaptive control. All the parameters have clear physical significance, and the selections of the initial values of the parameters are based on the stability conditions of the closed-loop system. Therefore, the selection of the parameters in the new model-free adaptive control does not depend entirely on trial and error but on regularity. By introducing the idea of internal model control in the new model-free adaptive control, the anti-disturbance performance of the closed-loop system is enhanced. Finally, simulation results for three complicated nonlinear systems show that the proposed model-free adaptive control is superior to the existing model-free adaptive control.

Keywords

• Model-free adaptive control
• data-driven
• discrete-time systems
• nonlinear control