Data-driven adaptive compensation control for a class of nonlinear discrete-time system with bounded disturbances

This paper considers the compensation control problem for a class of nonlinear discrete-time systems subject to bounded disturbances. With the help of the dynamic linearization technique (DLT), an equivalent data model to the unknown disturbed controlled plant is first established. Based on the data model, two data-driven controllers are designed through novel disturbance-related compact-form and partial-form DLT, which are equivalent to the unknown ideal compensation controller in theory. Adaptive gains designed for the proposed controllers are time-varying and are adaptively updated by directly utilizing the I/O data without involving any model information of the controlled plant, making both controllers purely data-driven adaptive disturbance compensation controllers. Further, in practice, unmeasurable disturbances are commonly encountered due to expensive measuring instruments, unreliable performance or large lags. Therefore, both proposed control laws provide solutions for measurable disturbance (MD) and unmeasurable disturbance (UD) in a unified framework, where the time-varying adaptive gains fuse more system dynamics when disturbance is completely unknown except for some boundedness. The stability of the proposed controllers are strictly guaranteed, and their effectiveness and applicability are verified by a numerical simulation and a distillation column.