An improved model-free adaptive control for nonlinear systems: An LMI approach

This paper proposes two model-free adaptive control (MFAC) schemes by using the linear matrix inequality (LMI) approach for the single-input single-output (SISO) and multi-input multi-output nonlinear (MIMO) systems, respectively. For each control scheme, with the aid of the dynamic linearization technique, the nonlinear system is transformed into an equivalent linear data model. In such a transformation, the nonlinear characteristic of systems is compressed into a time-varying parameter. Then, with the help of the introduction of the observer method, the tracking control problem can be converted into an optimization problem and the controller parameters can be obtained by using the LMI technique. This conversion cannot only reduce the complexity of the stability analysis but also find the appropriate controller parameters, especially for the MIMO case. Finally, three examples with comparisons are provided to illustrate the validity of the devised MFAC schemes. (c) 2023 Published by Elsevier Inc.

Automated summary

This paper proposes two model-free adaptive control (MFAC) schemes for single-input single-output (SISO) and multi-input multi-output (MIMO) nonlinear systems, respectively, using the linear matrix inequality (LMI) approach. The nonlinear system is transformed into an equivalent linear data model using the dynamic linearization technique, and the tracking control problem is converted into an optimization problem using the observer method. The controller parameters are obtained through the LMI technique, reducing the complexity of stability analysis and finding appropriate parameters for MIMO systems. Three examples are provided to demonstrate the effectiveness of the proposed MFAC schemes.