Stabilization of strict-feedback nonlinear systems with input delay using closed-loop predictors

Abstract

In this paper, we consider the control problem of strict-feedback nonlinear systems with time-varying input and output delays. The approach is based on the usual observer/predictor/feedback approach, but the novelty is the use of the closed-loop dynamics in the predictor. This approach allows to develop two designs, an instantaneous predictor and a delay differential equation-based predictor, that both attain the same performance in terms of system trajectories and input signal as in the case with no delays. The design based on delay differential equations allows to build a cascade of predictors to deal with arbitrarily large delay bounds. The resulting controller is much simpler to implement than classical infinite-dimensional predictors, and it is robust with respect to actuation and measurement disturbances. We illustrate the approach with an application to the control of a chaotic system with input delay

Robust controller design for input‐delayed systems using predictive feedback and an uncertainty estimator

“…The robustness of this technique to bounded parametric uncertainties was analyzed later in [10] and extended to unknown constant and time-varying delays in [11] and [12], respectively. Complementary results have been obtained in the discrete-time framework [13][14][15], and also for nonlinear systems [16][17][18][19][20], even when the plant is unstable. The aforementioned works were focused on proving the closed-loop stability.…”

Delay compensation for linear systems with both state and distinct input delays

“…Inserting these two controllers into system (1) gives exactly the closed-loop system (8), which is asymptotically stable according to Assumption 1. Thus, Problem 1 is solved by (10)- (11). However, controllers (10)-(11) need the future states of the system and are thus acausal.…”

“…Stability analysis and stabilization of time-delay systems are two fundamental problems and many important results have been obtained. For example, stability analysis for linear time-delay systems was investigated in the works of Bekiaris-Liberis and Krstic 4 and Seuret et al, 5 stabilization for linear time-delay systems was studied in the works of Liu and Hu 6 and Zhang et al, 7 the stabilization problem of linear time-invariant systems with distinct input delays was considered in the work of Tsubakino et al, 8 and fixed-time stabilization of linear control systems was investigated in the works of Polyakov et al 9,10 Stability and stabilization problems have also been extensively studied for nonlinear time-delay systems [11][12][13] and stochastic nonlinear time-delay system, 14 and particularly, global output feedback stabilization of nonlinear systems was addressed in the works of Lan and Li 15 and Wang et al 16 There are also many references dealing with various analysis and design problems for time-delay systems, for example, dissipativity analysis, 17,18 sampled-data control, 19 and reliable H ∞ control. 20 It is well known that memory and memoryless controllers are two different approaches for stabilization of input delayed systems.…”

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

“…This has been a matter of concern for some researchers,() as the discretization of the integral may lead to instability of the closed‐loop. In the work of Zhou et al, a first‐order truncated predictor that ignores the infinite‐dimensional part of the controller was proposed and extended later to include higher‐order terms in the work of Zhou et al An approach that avoids the use of distributed terms by introducing sequential predictors in observer form was introduced in the work of Besançon et al and further developed in the work of Najafi et al The advantage of avoiding distributed terms has been further exploited recently in the works of Léchappé et al, Cacace et al, Mazenc and Malisoff …”