Adaptive output feedback control for large‐scale time‐delay systems with output‐dependent uncertain growth rate

Abstract

In this work, the problem of adaptive state regulation is addressed via output feedback for a wide class of large-scale systems with strongly interconnected time-delay nonlinearities. A design approach of partially decentralized adaptive controller is proposed, which gives a novel pair of reduced-order observer and controller with nonidentifier-based double adaptive gains. Compared with the existing results, the growth restrictions imposed on the interconnections are relaxed, where the growth rate includes not only an unknown constant but also the nonpolynomial functions of system output. The double dynamic gains are capable of compensating both the uncertain nonpolynomial growth rate and the unknown time-varying delay. By constructing novel Lyapunov-Krasovskii functionals and combining dynamic-scaling technique with Barb ȃlat's lemma, it is shown that global adaptive state asymptotical regulation is achieved, that is all the closed-loop signals are bounded, and the states of system and observer tend to zero as time goes to infinity. Finally, a simulation example is given to illustrate the proposed control scheme is independent of time delay and well universal.

Multiple models for decentralised adaptive control of discrete‐time systems

“…Partially decentralised controllers are designed for output regulation. 25 A substantial volume of work carried out in the past was on continuous-time decentralised adaptive control, barring a few exceptions. [26][27][28][29] Researchers proposed globally stable adaptive laws under various assumptions on the unknown interconnection structures and bounds on unknown parameters.…”

A Global Control Strategy to Remove Slow Delay Conditions for Delayed Systems with Complicated Polynomial Terms

“…By constructing the state observer and presenting an adaptive regulation method, the authors in [15] discussed the control issue for switched timedelay systems. By utilizing the L-K functional method and double dynamic gains, the authors in [16] studied a largescale delayed model and designed a stable controller. When system delays do not satisfy this condition, i.e., they behave as nonslow delays, the existing methods cannot be applied to the system control.…”

Adaptive fault‐tolerant decentralized tracking control of switched stochastic uncertain nonlinear systems with time‐varying delay

“…Time-delay is one of the main reasons for the deterioration or even instability of the overall performance of the system. [35][36][37][38][39][40][41][42][43][44][45] In most cases, stability is the premise for the normal operation of the system. Therefore, the stability research of time-delay systems has attracted great attention of researchers.…”

“…In addition, the signal transmission at one or more positions of actual industrial equipment may be delayed in the measurement element or measurement process, control element, and actuator process (such as steam and fluid flow in the pipeline and electrical signal transmission on the long line), which is so‐called time‐delay. Time‐delay is one of the main reasons for the deterioration or even instability of the overall performance of the system 35‐45 . In most cases, stability is the premise for the normal operation of the system.…”