Parameter estimation in linear time invariant continuous systems

SUMMARY PARAMETER ESTIMATION IN LINEAR TIME-INVARIANT CONTINUOUS SYSTEMS Estimation of parameters in linear time-invariant continuous systems arising in different areas such as economic, electric, robotic and chemical applications. In these applications, estimation performance is very important for the systems to be controllable, observable and identifiable. In this dissertation, parameter estimation problem in linear time-invariant, continuous system is considered. A new method is introduced for estimating of parameters of state-space models of such systems from known input and noisy output data. The output of the system is expressed as a function of the input, the integral of the output, and the parameters. An objective function, defined as the error between model-predicted data and measurement data, is minimized by nonlinear least-squares methods, namely Marquardt- Levenberg, Gradient, Hessian-Gradient and PART AN algorithms. The performance of the proposed method was tested on various systems for different noise levels, different number of measurements, different input signals and different initial values. Results illustrates the accuracy and the validity of the proposed method. Key words: Linear time-invariant system, State model, Parameter estimation, Least- Squares method, Marquardt-Levenberg algorithm, Gradient algorithm, Hessian-Gradient algorithm, PART AN algorithm. VII