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Delay-Adaptive Linear Control$
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Yang Zhu and Miroslav Krstic

Print publication date: 2020

Print ISBN-13: 9780691202549

Published to Princeton Scholarship Online: January 2021

DOI: 10.23943/princeton/9780691202549.001.0001

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Basic Idea of Adaptive Control for Single-Input Systems

Basic Idea of Adaptive Control for Single-Input Systems

Chapter:
(p.35) Chapter Three Basic Idea of Adaptive Control for Single-Input Systems
Source:
Delay-Adaptive Linear Control
Author(s):

Yang Zhu

Miroslav Krstic

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691202549.003.0003

This chapter provides a variety of adaptive predictor control techniques to deal with different uncertainty collections from four basic uncertainties. These include delay, parameter, ODE state, and PDE state. In the presence of a discrete actuator delay that is long and unknown, but when the actuator state is available for measurement, a global adaptive stabilization result is obtainable. In contrast, the problem where the delay value is unknown, and where the actuator state is not measurable at the same time, is not solvable globally, since the problem is not linearly parameterized in the unknown delay. In this case, a local stabilization is feasible, with restrictions on the initial conditions such that not only do the initial values of the ODE and actuator state have to be small, but also the initial value of the delay estimation error has to be small (the delay value is allowed to be large but the initial value of its estimate has to be close to the true value of the delay).

Keywords:   adaptive predictor control techniques, delay, parameter, ODE state, PDE state, actuator delay, actuator state, global adaptive stabilization, local stabilization, delay value

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