Enhanced data-driven optimal iterative learning control for nonlinear non-affine discrete-time systems with iterative sliding-mode surface

Abstract

In this work, an enhanced data-driven optimal iterative learning control (eDDOILC) is proposed for nonlinear nonaffine systems where a new iterative sliding mode surface (ISMS) is designed to replace the traditional tracking error in the controller design and analysis. It is the first time to extend the sliding mode surface to the iteration domain for systems operate repetitively over a finite time interval. By virtual of the new designed ISMS, the control design becomes more flexible where both the time and the iteration dynamics can be taken into account. Before proceeding to the controller design, an iterative dynamic linear data model is built between two consecutive iterations to formulate the linear input-output data relationship of the repetitive nonlinear nonaffine discrete-time system. The linear data model is virtual and does not have any physical meanings, which is very different to the traditional mechanism mathematical model. In the sequel, the eDDOILC is proposed by designing an objective function with respect to the proposed two-dimensional ISMS. Rigorous proof is provided to show the convergence of the proposed eDDOILC method. Furthermore, the results have been extended to a multiple-input multiple-output (MIMO) nonaffine nonlinear discrete-time repetitive system. In general, the proposed eDDOILC is data-driven where no explicit model information is included. It is illustrated that the presented eDDOILC is effective when applied to the nonlinear nonaffine uncertain systems.