Abstract
This paper studies a mixed objective problem of minimizing a composite measure of thel 1, ℋ2, andl ∞-norms together with thel ∞-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 estabilished.
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Communicated by J. B. Pearson
This research was supported by the National Science Foundation under Grants No. ECS-92-04309, ECS-92-16690 and ECS-93-08481.
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Salapaka, M.V., Voulgaris, P.G. & Dahleh, M. Controller design to optimize a composite performance measure. J Optim Theory Appl 91, 91–113 (1996). https://doi.org/10.1007/BF02192284
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DOI: https://doi.org/10.1007/BF02192284