Constrained Adaptive Proportional Integral Tracking Control for Two-step Neural Network Models with Delays

Abstract

For the SDC problem, the following two problems still exist in PDF controller design:

1. Due to the lack of model knowledge, most published results only address linear precise models (see [61, 63, 64, 157, 161, 164]) that obviously cannot satisfy industrial demands. Furthermore, some nonlinear models discussed (see [58, 66, 73, 109, 183, 184, 196]) were also difficult to obtain through traditional identification approaches.

2. The constraint due to the PDF characteristics was neglected in most of the existing results (see [65, 157]). It is noted that without such a constraint, the weighting vector is irrelevant to a PDF obtained via B-spline models. In this case, the tracking objective of the output PDF cannot be achieved even if weight tracking is completed.

In order to overcome the above obstacles, in this chapter two-step NN models are applied to accomplish the SDC design problem using a constrained PI controller. After using B-spline NN approximation theory for the output PDF, we attempt to import time delay DNNs with undetermined parameters to identify the unknown nonlinear dynamic relationships. This represents a significant extension to the previous results. In the proposed method, an adaptive projection algorithm is utilized to compute the undetermined parameters related to the DNNs. Meanwhile, the PI control gains can be given based on a class of LMI algorithms. It will be shown that both the identification and tracking errors can converge to zero within a finite time using the Lyapunov stability criterion, and the state constraints can also be guaranteed simultaneously. It is noted that the proposed two-step NN approach has the independent significance in complex system control fields, and has also potential applications to other PI/PID type control problems.