Error Bounds for Identification of a Class of Continuous LTI Systems

Venkata Goutham Polisetty1, Santhosh Kumar Varanasi2, Phanindra Jampana1

  • 1Indian Institute of Technology Hyderabad
  • 2Indian Institute of Technology, Hyderabad.

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The main problem in identification of continuous LTI systems is the lack of derivative information of the outputs. If all the derivatives are known exactly, a least squares approach is sufficient to obtain the parameter estimates. In this paper, we propose a method which can provide theoretical bounds on the error in the parameter estimates assuming only a few derivatives are known accurately. The error bounds are given for the finite data case as opposed to the asymptotic regimes considered in existing identification approaches. The method is based on transforming the differential equation into the Laplace domain to obtain a linear-in-parameter form for the ODE parameters. As the system is not well conditioned, the method of Tikhonov Regularization is applied to find an approximate solution. Since, exact derivative information is seldom known in practice, B-spline approximation is incorporated in the simulation study where the accuracy of method is demonstrated.

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