30,195 research outputs found
On -extensions of the Hankel determinants of certain automatic sequences
In 1998, Allouche, Peyri\`ere, Wen and Wen considered the Thue--Morse
sequence, and proved that all the Hankel determinants of the period-doubling
sequence are odd integral numbers. We speak of -extension when the entries
along the diagonal in the Hankel determinant are all multiplied by~. Then we
prove that the -extension of each Hankel determinant of the period-doubling
sequence is a polynomial in , whose leading coefficient is the {\it only
one} to be an odd integral number. Our proof makes use of the combinatorial
set-up developed by Bugeaud and Han, which appears to be very suitable for this
study, as the parameter counts the number of fixed points of a permutation.
Finally, we prove that all the -extensions of the Hankel determinants of the
regular paperfolding sequence are polynomials in of degree less than or
equal to
Optimal adaptive control for a class of stochastic systems
We study linear-quadratic adaptive tracking problems for a special class of stochastic systems expressed in the state-space form. This is a long-standing problem in the control of aircraft flying through atmospheric turbulence. Using an ELS-based algorithm and introducing dither in the control law we show that the resulting control achieves optimal cost in the limit, while simultaneously the unknown parameters converge to their true value
Parameter Estimation of Switched Hammerstein Systems
This paper deals with the parameter estimation problem of the
Single-Input-Single-Output (SISO) switched Hammerstein system. Suppose that the
switching law is arbitrary but can be observed online. All subsystems are
parameterized and the Recursive Least Squares (RLS) algorithm is applied to
estimate their parameters. To overcome the difficulty caused by coupling of
data from different subsystems, the concept "intrinsic switch" is introduced.
Two cases are considered: i) The input is taken to be a sequence of independent
identically distributed (i.i.d.) random variables when identification is the
only purpose; ii) A diminishingly excited signal is superimposed on the control
when the adaptive control law is given. The strong consistency of the estimates
in both cases is established and a simulation example is given to verify the
theoretical analysis.Comment: 16 pages, 3 figures; Accepted for publication by Acta Mathematicae
Applicatae Sinica (http://link.springer.com/journal/10255
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