This paper studies a mixed objective problem of minimizing a composite measure of the l1, ℋ2, and l∞-norms together with the l∞-norm of the step response of the closed loop. This performance index can be used to generate Pareto-optimal solutions with respect to the individual measures. The problem is analyzed for discrete-time, single-input single-output (SISO), linear time-invariant systems. It is shown via Lagrange duality theory that the problem can be reduced to a convex optimization problem with a priori known dimension. In addition, continuity of the unique optimal solution with respect to changes in the coefficients of the linear combination that defines the performance measure is established.
- Duality theory
- Multiobjective control