Practical stabilization of nonlinear systems with state-dependent sampling and retarded inputs

Abstract

Abstract-A solution to the problem of stabilizing nonlinear systems with input with a constant pointwise delay and statedependent sampling is proposed. It relies on a recursive construction of the sampling instants and on a recent variant of the classical reduction model approach. State feedbacks without distributed terms are obtained. A lower bound on the maximal allowable delay is determined via a LyapunovKrasovskii analysis.

Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

“…Theorem 1: Consider the closed-loop system consisting of the plant (13)-(15) and the control laws (42), (17)- (19). Under Assumptions 1, 2, and 3, there exists a class KL function β such that for all initial conditions X 0 ∈ R n and u i 0 ∈ C[0, D i ], i = 1, .…”

“…a) Background and Motivation: Despite the recent outburst in the development of predictor-based control laws for nonlinear systems with input delays [5], [6], [7], [8], [9], [10], [11], [13], [14], [15], [16], [17], [26], [27], [28], [29], [30], [31], [32], [35], [36], [37], [42], [43], [44], [45], [46], the problem of the systematic predictor-feedback stabilization of multi-input nonlinear systems with, potentially different, in each individual input channel, long input delays, has remained, heretofore, untackled, although the problem was solved in the linear case in the early 1980s [4] (see also [41]). In this article, we address the problem of stabilization of multi-input nonlinear systems with distinct input delays of arbitrary length and develop a nonlinear version of the prediction-based control laws developed in [4] and recently in [53], [54] for the compensation of input delays in multi-input linear systems.…”

Sampled-data stabilisation of a class of state-delayed nonlinear dynamics

“…Exploiting sampling to control systems with delayed inputs is a well known practice which has found renewed interest in the current literature ( [8], [9], [10], [11], [12]). The present work follows these lines.…”

Predictor-feedback stabilization of multi-input nonlinear systems

“…The Dj-time units ahead predictors of the state X, namely Pj, given in (3)- (5), and their equivalent representation by the PDE states pj, given in (17)- (19), based on the transport-PDE equivalent of the actuator states defined in (14)- (15). The control laws Uj are defined in (2) in terms of Pj and can be written equivalently as in (42) in terms of pj.…”

“…a) Background and Motivation: Despite the recent outburst in the development of predictor-based control laws for nonlinear systems with input delays [5], [6], [7], [8], [9], [10], [11], [13], [14], [15], [16], [17], [26], [27], [28], [29], [30], [31], [32], [35], [36], [37], [42], [43], [44], [45], [46], the problem of the systematic predictor-feedback stabilization of multi-input nonlinear systems with, potentially different, in each individual input channel, long input delays, has remained, heretofore, untackled, although the problem was solved in the linear case in the early 1980s [4] (see also [41]). In this article, we address the problem of stabilization of multi-input nonlinear systems with distinct input delays of arbitrary length and develop a nonlinear version of the prediction-based control laws developed in [4] and recently in [53], [54] for the compensation of input delays in multi-input linear systems.…”