Determination of Optimal Inputs for Precise Parameter Estimation and Model Discrimination

3 Determination of Optimal Inputs for Precise Parameter Estimation and Model Discrimination 

Murray and Reiff(1984) showed that the use of an optimally selected square wave for the input variables can offer considerable improvement in parameter estimation. Of course, it should be noted that the use of constant inputs is often 

For precise parameter estimation, we need to solve several optimal control problems each corresponding to a grid point of the operability region. The operability region is defined now by the potential values of the initial state (x0). A particular optimal control problem can be formulated as follows, 

Given the governing differential equations (the model) and the initial conditions, xo determine the optimal inputs, u(t), so that the determinant (for the volume criterion) or the smallest eigenvalue (for the shape criterion) of matrix Ane v (given by Equation 12.18) is maximized 

Obviously this optimal control problem is not a typical textbook problem . It is not even clear whether the optimal solution can be readily computed. As a result, one should consider suboptimal solutions. 

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