Learning Based Nonlinear Internal Model Control

Abstract

In this paper, we propose a learning based nonlinear internal model control approach for nonlinear dynamic systems with non-parametric uncertainties. When nonlinear non-parametric uncertainties exist both in the plant and exogenous system, it is difficult to apply the classical IMC. On the other hand, a major class of the neutrally stable exogenous systems is the periodic systems which generate periodic output signals. When the periodicity of an exogenous system is known a priori, and the resulting internal model is also periodic in nature, a learning mechanism can be constructed to update the control profile in a cyclic manner. The learning mechanism, using memory components, stores the tracking information of the preceding cycle and updates the memory cycle after cycle. By virtue of the memory components, the internal model corresponding to the highly nonlinear uncertain plant and exogenous system, can be approximated asymptotically. In this work, with the help of composite energy function, a robust feedback control is integrated with the learning. The robust control ensures the internal signal boundedness of the control system in the large, meanwhile the learning mechanism works to approximate the inverse control, in the sequel the internal model. The effectiveness of the proposed method is demonstrated by an illustrative example.