Optimization-Based Design for Data-Driven Control of SISO Nonaffine Nonlinear Systems

For the adaptive tracking of nonaffine nonlinear systems, the unknown nonlinear dynamics is regarded as one of the essential factors that may hinder the effective controller establishment and the tracking precision improvement. To tackle this difficulty for a class of single-input single-output (SISO) nonaffine nonlinear systems, we develop an optimization-based design method for data-driven control to achieve the desired tracking objective in the presence of the time-varying reference trajectory. It is shown that the proposed data-driven controller can render the tracking error to strictly converge, regardless of the SISO unknown nonlinear dynamics. In addition, thanks to a novel grouping-based contraction mapping method and properties of non-negative matrices, the boundedness of the I/O sequence is established. Simulations are implemented to verify that the proposed data-driven controller can realize the anticipated tracking performance for nonlinear systems.