Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold

Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is general...

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Published in:	IEEE transactions on automatic control Vol. 57; no. 5; pp. 1141 - 1154
Main Authors:	Karafyllis, I., Krstic, M.
Format:	Journal Article
Language:	English
Published:	New York, NY IEEE 01.05.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Applied sciences Asymptotic properties Asymptotic stability Computer science; control theory; systems Computer systems and distributed systems. User interface Control system analysis Control system synthesis Control systems Control theory Control theory. Systems Delay Differential equations Exact sciences and technology Feedback Feedback stabilization Laws Networked control systems nonlinear control Nonlinear systems sampled-data systems Sampling Software Stabilization Studies Sufficient conditions time-delay systems Sampled system nonlinear control Non linear control Delay control Feedback regulation Non holonomic system Continuous time Delay system Distributed system Non linear system sampled-data systems Asymptotic stability Linear time invariant system time-delay systems Continuous control Global stabilization Distributed control Mobile agent Delay time Asymptotic approximation Feedforward Sampling Feedback stabilization Delay effect
ISSN:	0018-9286, 1558-2523
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Abstract	Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this paper, we present two general results that address these example problems as special cases. First, we present global asymptotic stabilizers for forward complete systems under arbitrarily long input and output delays, with arbitrarily long sampling periods, and with continuous application of the control input. Second, we consider systems with sampled measurements and with control applied through a zero-order hold, under the assumption that the system is stabilizable under sampled-data feedback for some sampling period, and then construct sampled-data feedback laws that achieve global asymptotic stabilization under arbitrarily long input and measurement delays. All the results employ "nominal" feedback laws designed for the continuous-time systems in the absence of delays, combined with "predictor-based" compensation of delays and the effect of sampling.
AbstractList	Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this paper, we present two general results that address these example problems as special cases. First, we present global asymptotic stabilizers for forward complete systems under arbitrarily long input and output delays, with arbitrarily long sampling periods, and with continuous application of the control input. Second, we consider systems with sampled measurements and with control applied through a zero-order hold, under the assumption that the system is stabilizable under sampled-data feedback for some sampling period, and then construct sampled-data feedback laws that achieve global asymptotic stabilization under arbitrarily long input and measurement delays. All the results employ "nominal" feedback laws designed for the continuous-time systems in the absence of delays, combined with "predictor-based" compensation of delays and the effect of sampling.
Author	Krstic, M. Karafyllis, I.
Author_xml	– sequence: 1 givenname: I. surname: Karafyllis fullname: Karafyllis, I. email: ikarafyl@enveng.tuc.gr organization: Dept. of Environ. Eng., Tech. Univ. of Crete, Chania, Greece – sequence: 2 givenname: M. surname: Krstic fullname: Krstic, M. email: krstic@ucsd.edu organization: Dept. of Mech. & Aerosp. Eng., Univ. of California at San Diego, La Jolla, CA, USA
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Keywords	Sampled system nonlinear control Non linear control Delay control Feedback regulation Non holonomic system Continuous time Delay system Distributed system Non linear system sampled-data systems Asymptotic stability Linear time invariant system time-delay systems Continuous control Global stabilization Distributed control Mobile agent Delay time Asymptotic approximation Feedforward Sampling Feedback stabilization Delay effect
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Snippet	Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is...
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SubjectTerms	Applied sciences Asymptotic properties Asymptotic stability Computer science; control theory; systems Computer systems and distributed systems. User interface Control system analysis Control system synthesis Control systems Control theory Control theory. Systems Delay Differential equations Exact sciences and technology Feedback Feedback stabilization Laws Networked control systems nonlinear control Nonlinear systems sampled-data systems Sampling Software Stabilization Studies Sufficient conditions time-delay systems
Title	Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold
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