2012
DOI: 10.1002/acs.2378
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Positive invariant set estimation of adaptive controller in the presence of input saturation

Abstract: For a class of linear dynamical systems with constant unknown parameters, an L 1 adaptive control scheme is developed that provides stable adaptation in the presence of input magnitude constraints. Whereas for open-loop stable systems the results are global, for open-loop unstable systems, the problem of nonconservative estimation of the nonempty positive invariant set is cast into an LMI framework, which can be efficiently solved numerically via convex optimization. To achieve this, a standard result toward i… Show more

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Cited by 15 publications
(3 citation statements)
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“…Lemma 3: Given the system in (22) and the L 1 adaptive controller defined via (24)(25)(26)(27)(28)(29), if ||ω τ || L∞ ≤ ρ and ||u a(c)τ || L∞ ≤ ρ u , then, the prediction errorω(t)is uniformly bounded as (59), as shown at the bottom of this page.…”
Section: ) Reference Systemmentioning
confidence: 99%
See 1 more Smart Citation
“…Lemma 3: Given the system in (22) and the L 1 adaptive controller defined via (24)(25)(26)(27)(28)(29), if ||ω τ || L∞ ≤ ρ and ||u a(c)τ || L∞ ≤ ρ u , then, the prediction errorω(t)is uniformly bounded as (59), as shown at the bottom of this page.…”
Section: ) Reference Systemmentioning
confidence: 99%
“…Theorem 1: Consider the closed-loop reference system in (33-35) and the closed-loop system consisting of the system in (22) and the L 1 adaptive controller in (24)(25)(26)(27)(28)(29) subject to the L 1 -norm condition (37). If the adaptive gain is chosen to verify the design constraints ≥ λ max (P)…”
Section: ) Reference Systemmentioning
confidence: 99%
“…Behandlung von Totzeiten und Aktuatorlimitierungen Die Theorie der L 1 -adaptiven Regelung erlaubt es auch Totzeiten und Aktuatorlimitierungen zu behandeln, siehe [42,71]. Gerade bei einer Anwendung am Quadrokopter sind auch diese Aspekte von Interesse, waren jedoch im Rahmen dieser Arbeit nicht mehr zu berücksichtigen.…”
Section: Weitere Forschungunclassified