A New Criterion for Optimal Parameter Identification

The synthesis of inputs for optimal parameter identification involves the optimization of a suitable criterion so that the identification experiment provides maximum information. A measure of the information content of an identification experiment is the information matrix (IM). Here, it is proven that for continuous deternministic systems linear in the unknown parameters the convergence rate is determined by the condition number of the IM. Based on this result, a new criterion is presented, the C-Optimality Criterion. With this formulation, the optimal input design (OID) for parameter identification is reduced to solving a nonlinear optimal control problem (NOCP). Solving the NOCP is one of the most time consuming tasks in the identification experiment. Therefore, it is evident that for the practical use of OID methods one needs to provide an efficient and simple algorithm for solving the optimization problem. However, a general analytic expression for the condition number does not exist. This implies that the cost function and its Jacobian matrix have to be evaluated numerically. A new analytic scalar cost function is proposed to measure the IM conditioning. However, the result of the NOCP is suboptimal, unless the solution has a condition number close to one. A simple example is presented to illustrate the theory and to show how optimal inputs improve the parameter convergence rate.