Global uniqueness tests for H∞ optima

Optimization of sup norm type performance functions over the space of H^∞ functions is central to the subject of H^∞ design. Problems with a large amount of plant uncertainty are often highly nonconvex and therefore may have many solutions. In this article, even for highly nonconvex problems, we give a test one can perform, once a local optimum f* has been computed, to see if it is a global optimum. The uniqueness phenomena we discovered uses H^∞ properties heavily and are considerably stronger than what occurs in other types of general optimization. One of the least intuitive properties of SISO control is that a (local) optimum for a carefully set up H^∞ problem, even with large amounts of plant uncertainty, is unique. Such problems can be quite nonconvex so the fact is surprising. While the result is false in general for MIMO control, in this note we are describing MIMO situations where uniqueness holds. The setting in this paper is simultaneous (Pareto) optimization of several competing performances Γ₁ ,...,Γ_e and we obtain uniqueness results for its solutions