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Second level adaptation using multiple models for the adaptive control of linear systems with unknown parameters was introduced in [1], and its robustness properties were discussed in [2]. In both cases, the plant, the identification models, and the reference model were assumed to be described by state equations in companion form, with all state variables accessible.
A new approach, described as second level adaptation, was introduced in [1] for the control of unknown linear time-invariant plants using multiple identification models. If θp ∈ Rn, the unknown parameter vector of an LTI system lies in the convex hull P(t0) of (n+1) vectors θi(t0) (initial values of adaptive vectors) in parameter space, it was shown that it lies also in the convex hull of θi(t)(i...
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