Adaptive Model-Free Control Based on an Ultra-Local Model With Model-Free Parameter Estimations for a Generic SISO System

In this paper, a new structure to design model-free control (MFC) based on the ultra-local model is presented for an unknown nonlinear single-input single-output dynamic system. The proposed structure includes two adaptive laws corresponding to the unknown linear and nonlinear terms. Utilizing the adaptive law for linear term, the controller gain is going to be updated online using a differential Riccati equation. Subsequently, the control policy which includes an optimal term as well as a term for compensating the system unknown dynamics is generated. Here, the two proposed adaptive laws are model-free estimation algorithms, in which the need for any regressor parameter and also the persistent excitation condition is eliminated. Finally, two simulation studies are presented to show that the proposed adaptive MFC (AMFC) policy outperforms the two well-known controllers. Moreover, the AMFC is applied on a Duffing-Holmes chaotic oscillator plant and the convincing performance of the algorithm is observed through the simulation results.