Multiobjective control: an overview

An overview of a number of approaches to the multiobjective control problem is given. In practice, this problem usually boils down to a mixed-norm optimization, where traditionally the norms of interest are H₂, H_∞ and l₁. To capture different, often conflicting, design specifications a single-norm form is usually not enough and therefore a mixed-norm formalism combining these norms would be of considerable interest. Although it would be nice to have all three norms present, most approaches focus on the two-norm problem. Frequently encountered is the H₂/H_∞ mixed-norm optimization problem, but combinations of l₁ and the other two norms are starting to get more attention. It will be seen that the solution to the mixed-norm optimization problem has not yet reached a final shape, since most methods still exhibit problems, like not being able to find a solution if performance specifications are tight, or generating high-order or too conservative controllers, etc