Decentralized Intermittent Feedback Adaptive Control of Non-triangular Nonlinear Time-varying Systems

TL;DR

This paper introduces two decentralized adaptive control schemes for interconnected nonlinear systems with non-triangular uncertainties and intermittent feedback, broadening applicability and ensuring stability with bounded inter-event times.

Contribution

The work develops novel backstepping-based adaptive control methods that handle non-triangular uncertainties and intermittent feedback without derivative of parameters, expanding existing stabilization techniques.

Findings

Both schemes guarantee global uniform boundedness of signals.

The proposed methods ensure a positive lower bound on inter-event intervals.

Numerical simulations confirm the effectiveness and advantages of the control schemes.

Abstract

This paper investigates the decentralized stabilization problem for a class of interconnected systems in the presence of non-triangular structural uncertainties and time-varying parameters, where each subsystem exchanges information only with its neighbors and only intermittent (rather than continuous) states and input are to be utilized. Thus far to our best knowledge, no solution exists priori to this work, despite its high prevalence in practice. Two globally decentralized adaptive control schemes are presented based on the backstepping technique, the first one is developed in a continuous fashion by combining the philosophy of the modified congelation of variables based approach with the special treatment of non-triangular structural uncertainties, which avoids the derivative of time-varying parameters and eliminates the limitation of the triangular condition, thus largely broadens the scope of application. By making use of the important property that the partial derivatives of the constructed virtual controllers in each subsystem are all constant, the second scheme is developed through directly replacing the states in the preceding scheme with the triggered ones. Consequently, the non-differentiability of the virtual control stemming from intermittent state feedback is completely obviated. The internal signals under both schemes are rigorously shown to be globally uniformly bounded with the aid of several novel lemmas, while the stabilization performance can be enhanced by appropriately adjusting design parameters. Moreover, the inter-event intervals are ensured to be lower-bounded by a positive constant. Finally, numerical simulation verifies the benefits and efficiency of the proposed method.