##
**Taylor series approach to system identification, analysis and optimal control.**
*(English)*
Zbl 0561.93018

The problems of system identification, analysis and optimal control have been recently studied using orthogonal functions. The specific orthogonal functions used up to now are the Walsh, the block-pulse, the Laguerre, the Legendre, the Chebyshev, the Hermite and the Fourier functions. In the present paper solutions to these problems are derived using the Taylor series expansion. The algorithms proposed here are similar to those already developed for the orthogonal functions; however, due to the simplicity of the operational matrix of integration, the Taylor series presents considerable computational advantages compared with the other polynomial series, provided that the input and the output signals may be assumed to be analytic functions of t.

### MSC:

93B30 | System identification |

41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |

44A45 | Classical operational calculus |

93C05 | Linear systems in control theory |

93B40 | Computational methods in systems theory (MSC2010) |

PDF
BibTeX
XML
Cite

\textit{S. G. Mouroutsos} and \textit{P. D. Sparis}, J. Franklin Inst. 319, 359--371 (1985; Zbl 0561.93018)

Full Text:
DOI

### References:

[1] | Chen, C.F.; Hsiao, C.H., Design of piecewise constant gains for optimal control via Walsh functions, IEEE trans. aut. contr., Vol. 20, 596-603, (1975) · Zbl 0317.49042 |

[2] | Sannuti, P., Analysis and synthesis of dynamic systems via block-pulse functions, Proc. IEE, Vol. 124, 569-571, (1977) |

[3] | King, R.W.; Paraskevopoulos, P.N., Parametric identification of discrete-time SISO systems, Int. J. control, Vol. 30, 1023-1029, (1979) · Zbl 0418.93026 |

[4] | Hwang, C.; Guo, T., Parameter identification of a class of time-varying systems via orthogonal shifted Legendre polynomials, J. franklin institute, Vol. 318, No. 1, 59-69, (1984) · Zbl 0589.93012 |

[5] | Paraskevopoulos, P.N., Chebyshev series approach to system identification, analysis and optimal control, J. franklin inst., Vol. 316, 135-157, (1983) · Zbl 0538.93013 |

[6] | P.N. Paraskevopoulos, P.D. Sparis and S.G. Mouroutsos, “Fourier series approach to system identification, analysis and optimal control”,Proc. AMSE ’83, Conference on Modelling and Simulation, Nice, France. · Zbl 0558.44004 |

[7] | Brewer, J.W., Kronecker products and matrix calculus in system theory, IEEE trans. circuits syst., Vol. 25, 772-781, (1978) · Zbl 0397.93009 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.