A New Neural Dynamic Learning Framework for Discrete-Time Strict-Feedback Systems: Internal Interaction-Based Weight Adaptive Laws

This article investigates internal interaction-based dynamic learning control (LC) for uncertain discrete-time strict-feedback systems. On the basis of predict technology, the original system is converted into a common
$n$
-step-ahead input–output predict model. The predict model causes every estimated neural weight to converge to
$n$
different constants using the existing control framework. To solve such a problem, the predict model is further decomposed into
$n$
one-step-ahead subsystems, which can be viewed as
$n$
independent agents. Subsequently, the distributed cooperative weight adaptive laws are designed by introducing an undirected and connected interconnection topology among subsystems. By constructing the variable relationship between the subsystems and the
$n$
-step-ahead predict model, a new internal weight interaction-based neural dynamic LC framework is proposed for the whole closed-loop system, in which estimated weights at different times share their weight knowledge. The proposed framework ensures the ultimately uniform boundedness of the closed-loop system and achieves the excellent control performance. By combining the consensus theory and a cooperative persistent excitation condition, every estimated weight along the neural input orbit is verified to exponentially converge to a close vicinity of a unique ideal constant, rather than
$n$
different constants. Consequently, the developed LC framework facilitates constant weights storage, saves the knowledge storage space, and improves the robustness of knowledge utilization. These characteristics are verified by simulation results.