Adaptive Statistical Tracking Control Based on Two-step Neural Networks with Time Delays

Abstract

AbstractMotivated by Chapter 6 and Chapter 8, in this chapter two-step NN are applied to solve the STC problem. Similarly to the output PDF tracking control problem, after using B-spline NN approximation theory for the integrated performance function in the context of the entropy and mean, it is shown that the above STC problem can be transformed into a tracking problem for the weighting dynamics. However, due to lack of model knowledge, most published results only concern linear and precise models and some nonlinear models discussed were also difficult to obtain through traditional identification approaches. In this chapter, 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, the adaptive laws and LMI obtained can guarantee that the identification error converges to zero within a finite time. Based on adaptive projection arithmetic (see [170, 171]) and VSC theory (see [21, 104, 152]), a dynamic state feedback controller is developed in which the weight vectors can be made to follow the outputs of a reference model with a fast response. Finally, simulations are provided to show the effectiveness of the proposed results.KeywordsControl InputTracking ControlModel Reference Adaptive ControlCompensation TermSatisfactory Tracking PerformanceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.