Robust Nash Strategy for Uncertain Delay Systems with LSTM and Its Application for TCP/AQM Congestion Control

Abstract

In this paper, we propose a robust Nash strategy for a class of uncertain delay systems (UDSs) via static output feedback (SOF) with additive gain variation based on long short-term memory (LSTM), which is known as one of the recurrent neural networks. After establishing the extended bounded real lemma for UDS, the conditions for the existence of a robust Nash strategy set are determined by means of matrix inequalities. It is shown that input delay can be compensated because the LSTM has the powerful capability of learning past state information. It should be noted that the proposed LSTM can be worked as the additive gain variation and the stability for the closed-loop UDS is guaranteed. In order to solve the SOF problem, an heuristic algorithm is developed based on the algebraic equations and the linear matrix inequalities (LMIs). In particular, it is shown that robust convergence is guaranteed under a new convergence condition. Finally, a practical numerical example based on the congestion control for active queue management is provided to demonstrate the reliability and usefulness of the proposed design scheme.