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MIMO optimal control design: the interplay between the ℋ2 and the l1 norms

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3 Author(s)
Salapaka, M.V. ; Dept. of Electr. & Comput. Eng., Iowa State Univ., Ames, IA, USA ; Dahleh, M. ; Voulgaris, P.G.

We consider controller design methods which can address directly the interplay between the ℋ2 and l1 performance of the closed loop. The development is devoted to multi-input/multi-output (MIMO) systems. Two relevant multi-objective performance problems are considered each being of interest in its own right. In the first, termed as the combination problem, a weighted sum of the l1 norms and the square of the ℋ2 norms of a given set of input-output transfer functions constituting the closed loop is minimized. It is shown that, in the one-block case, the solution can be obtained via a finite-dimensional quadratic optimization problem which has an a priori known dimension. In the four-block case, a method of computing approximate solutions within any a priori given tolerance is provided. In the second, termed as the mixed problem, the ℋ2 performance of the closed loop is minimized subject to an l1 constraint. It is shown that approximating solutions within any a priori given tolerance can be obtained via the solution to a related combination problem

Published in:

Automatic Control, IEEE Transactions on  (Volume:43 ,  Issue: 10 )