Controller design to optimize a composite performance measure
This paper studies a mixed objective problem of minimizing a composite measure of the \(l_1\)-norm, the \(H_2\)-norm, and the \(l_\infty\)-norms of the step and pulse responses respectively of the closed loop over all stabilizing controllers. Employing a variant of the Kuhn-Tucker-Lagrange duality theorem, it is shown that the problem is equivalent to a finite-dimensional convex optimization problem with an a priori known dimension. The solution is unique and represents a Pareto-optimal point with respect to the individual measures involved. It is also shown that the optimal solution is continuous with respect to changes in the coefficients of the composite measure. The problem is analyzed for discrete-time, single-input single-output, linear time-invariant systems.
scientific article; zbMATH DE number 1031434
scientific article