Design of Observer by Using the Degree of Optimality

概要

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The problem of designing optimal observers of order n-m and n for an nth order plant with m outputs is considered. The cost functional for the regulator is the usual integral quadratic form. In this paper, the case of the known means and covariances of the initial conditions, and thee case of the uniform distribution of the initial conditions are discussed by using the degree of optimality which quantitatively measures the total performance of the control system.The necessary condition is derived for the optimal observer of order n-m. This condition is much simpler than the one Newmann derived when the means and covariances of the initial conditions are known. Some examples show that this necessary condition is useful.In the latter half of this paper, the observer of order n is considered. It is shown that the cost can be decreased by making the real part of some eigenvalues of the observer approach minus infinity while keeping the eigenvalues in a certain mutual relation. For this case, Bongiorno and Youla showed that the cost would be increasingly large when the real part of all the eigenvalues of the observer approach minus infinity.
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