Some remarks on a conjecture in parameter adaptive control |
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Authors: | Roger D Nussbaum |
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Affiliation: | Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA |
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Abstract: | A.S. Morse has raised the following question: Do there exist differentiable functions with the property that for every nonzero real number λ and every (x0, y0) ∈ 2 the solution (x(t),y(t)) of , , , is defined for all t ? 0 and satisfies and y(t) is bounded on 0,∞)? We prove that the answer is yes, and we give explicit real analytic functions f and g which work. However, we prove that if f and g are restricted to be rational functions, the answer is no. |
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Keywords: | Parameter adaptive control |
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