Effective diagonalization strategies for the solution of a class of optimal design problems

It is shown that it is possible to obtain optimal diagonalization strategies for the discretization of semiinfinite minimax optimal design problems. Both exact and approximate methods for the computation of these optimal diagonalization strategies are proposed. The algorithms for computing approximate diagonalization strategies yield very good approximations in much less computing time than needed to compute an optimal diagonalization strategy exactly. The proposed diagonalization strategies can be implemented by using estimation schemes to obtain approximations to the various quantities which determine an optimal strategy. Experimental results, involving the solution of optimal loop-shaping problems for multivariable linear feedback systems, show that the use of these implementable strategies leads to considerable savings in computer time over alternative approaches.>