Error-based adaptive optimal tracking control of nonlinear discrete-time systems

In this paper, for the output tracking problem of nonlinear discrete-time systems, a performance index is newly defined using the adaptive dynamic programming (ADP) technique to completely eliminate tracking errors in theory. In contrast to traditional definitions of performance indices in other ADP-based methods, the proposed performance index is not only designed from the perspective of output tracking errors but also introduced errors of system states and control inputs at adjacent stages, which is suitable for practical situations in many industrial applications, such as the alumina production, the flotation process, and the mineral grinding process. We proved that the obtained controller can make the system output fully track the given reference trajectory by applying the iterative criteria of the ADP technique. In addition, the proposed algorithm was implemented using a data-driven technique and neural networks to avoid analyzing and deducing the complicated dynamics of actual industrial processes. Finally, using historical data for a forced-circulation evaporation system in the alumina production process, the effect of the proposed approach was verified through a numerical simulation and compared with that of the proportional-integral controller.