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Compensation of time‐varying input delay for discrete‐time nonlinear systems[Note ‡. ‡ This work has been conducted during the first ...]
Author(s) -
Choi JoonYoung,
Krstic Miroslav
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3382
Subject(s) - control theory (sociology) , discrete time and continuous time , bounded function , nonlinear system , compensation (psychology) , controller (irrigation) , signal flow graph , computer science , mathematics , lti system theory , linear system , control (management) , engineering , mathematical analysis , statistics , physics , quantum mechanics , artificial intelligence , psychoanalysis , electrical engineering , agronomy , biology , psychology
Summary We consider general discrete‐time nonlinear systems (of arbitrary nonlinear growth) with time‐varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete‐time systems, an analogous restriction would be that the input delay is non‐increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous‐time case, the predictor feedback law in the discrete‐time case is explicit. We specialize the result to linear time‐invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges. Copyright © 2015 John Wiley & Sons, Ltd.