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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Veröffentlicht in:IEEE transactions on automatic control Jg. 57; H. 5; S. 1141 - 1154
Hauptverfasser: Karafyllis, I., Krstic, M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.05.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
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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Zusammenfassung: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2170451