Stabilization of a chain of three integrators by a feedback in the form of nested saturators

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The problem of stabilizing a chain of three integrators subject to a phase constraint by a continuous constrained control is considered. The application of a feedback in the form of nested saturators results in study of a switching system. Necessary conditions of local stability are established. A Lyapunov function is constructed by means of which it is proved that the necessary conditions are sufficient for global stability of the closed-loop system. The discussion is illustrated by numerical examples.

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Sobre autores

Yu. Morozov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Autor responsável pela correspondência
Email: tot1983@inbox.ru
Rússia, Moscow

A. Pesterev

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Email: alexanderpesterev.ap@gmail.com
Rússia, Moscow

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1. JATS XML
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2. Formula 4.1

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3. Formula 4.2

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4. Formula 4.3

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5. Formula 4.4

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6. Fig. 1. Partition of the phase plane into sets D1, D2, D3

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7. Fig. 2. Level surface of the Lyapunov function (4.1)

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8. Fig. 3. Intersection of invariant regions and Π

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9. Fig. 4. Intersection of invariant regions and Π

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10. Fig. 5. Graphs of the time dependences of the deviation x1(t) (1), speed x2(t) (2), acceleration x3(t) (3) and control U(t) (4)

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