On Structure Determination for Polynomial Input-Output Differential Systems,
BROWN UNIV PROVIDENCE RI DIV OF ENGINEERING
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The problem of structure determination for a deterministic class of polynomial input-output differential systems is formulated as a minimum norm-discrete time optimal control problem. The order of the differential equation and the degrees of the polynomials involving the input-output variables play the role of multiple discrete-times while the coefficient parameters play the role of a discrete control variable. The basis of the parameter identification techniques is Shinbrots method of moment functionals using linear combinations of commensurable sinusoids as the modulating functions. Given the system input-output data on a finite time interval, the underlying computations involve calculating a finite set of Fourier series coefficients or moments formed from the data, which can be efficiently carried out via and FFT algorithm, followed by a sequence of singularity tests performed on a controllability type Gram determinant that arises for the formulation.
- Theoretical Mathematics