Numerical Solution of a Two-Disk Problem
S. Norman and S. Boyd
Recent Advances in Robust Control, P. Dorato and R. K. Yedavalli, editors, IEEE Press, pp.285-287, June 1990. Also appeared in Proceeding of the American Control Conference, pp.1745-1747, June 1989.
A multidisk problem in frequency domain control system synthesis is a problem in which the designer wishes to find a feedback compensator that minimizes the H_infty-norm of a certain transfer matrix related to the system being designed, subject to constraints on the H_infinity-norms of one or more other transfer matrices related to the system. It is shown that while multidisk problems may not have analytical solutions, that can often be posed as infinite-dimensional convex programming problems, and so can be readily solved numerically. A program called qdes can be used to generate and solve finite-dimensional approximations to such infinite-dimensional programming problems. It is used to solve the two-disk problem considered by S. Boyd et al. (IEEE Trans. Autom. Control, vol.AC-33, no.3, p.268-83, Mar. 1988). The optimal performance index is found to be over four times better than the approximate solution found previously.