Optimal Input Design for Active Parameter Identification of Dynamic Nonlinear Systems

There are many important aspects to be considered while designing optimal excitation signal for system identification experiment in control applications. Active parameter identification is an important issue in system and control theory. In this dissertation, the problem of optimal input design for active parameter identification of dynamic nonlinear system is addressed. Real life physical systems are identified by excitation with a suitable input signal and observing the resulting output behavior of the system. It is important to choose the input signal intelligently in the sense that it is responsible to determine the accuracy and nature of the unknown system characteristics. This leads to a spurred interest in designing such an optimal excitation signals that can yield maximal information from the identification experiment. The information obtained from parameter identification is usually not accurate due to incomplete knowledge of the system, disturbance as exogenous inputs and noisy measurements. Hence, the input spectrum is designed in such a way that it can improve the system performance and shape the quality of obtained information. A welldesigned input signal can maximize the amount of information and reduce the experimental cost and time. The input signal is usually given some a-priori characteristics (knowledge on the pdf) so that “excitation” of the system is guaranteed. In this thesis, a closed-loop method is investigated which is able to improve the parameter identification on the basis of the actual system’s behavior. The effectiveness of the proposed algorithm is presented by the experimental results which corresponds to the perfect identification of the unknown parameter vector. The major technical contribution of this work is to propose an optimal feedback input design method for active parameter identification of dynamic nonlinear systems. The proposed framework can design such optimal excitation signals, considering the information from the identified parameters, that can maximize the amount of information from the identified parameters, guarantee to meet the specified control performance and minimize some cost function of the error covariance matrix of the identified parameters. The problem is formulated in a receding horizon framework where extended Kalman filter is used for system identification and the optimal input is designed in a nonlinear model predictive control framework. In order to carry out a comparison study, also Unscented Kalman Filter and Gaussian Sum Filter are used for the active parameter identification of dynamic nonlinear system. Towards this end, a suitable optimality criterion related to the unknown parameters is proposed and motivated as an information measure. The aim of the optimal input design is to yield maximal information from the unknown system by minimizing the cost related to the unknown parameters while maintaining some process performance and satisfying the possible constraints. Simulations are performed to show the effectiveness of the proposed algorithm.