What is it about?
This Note proposes a passivity-based adaptive control strategy derived upon the simple adaptive control (SAC) theory. The stability of the passivity-based adaptive system is guaranteed through the Lyapunov direct method and LaSalle’s invariance principle for nonautonomous systems, by applying the almost strictly passive conditions. These conditions are herein demonstrated to be satisfied by modeling both the Clohessy–Wiltshire and the double-integrator relative dynamics models as square linear time-invariant systems with a scaled position-to-velocity output matrix. In addition, based on recent development in the area of nonlinear stability, this Note clarifies the use of LaSalle’s invariance principle (as opposed to the widely used Barbalat’s lemma) for this particular problem, where the Lyapunov derivative function is negative-semidefinite.
The following have contributed to this page: Dr Itzhak Barkana
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