Transfer Function Optimization Procedure for the H 2/H ∞ Problem

G.O. Corrêa and D. M. Sales
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G.O. Corrêa: National Laboratory for Scientific Computing, Petrópolis
D. M. Sales: Army Polytechnic School

Journal of Optimization Theory and Applications, 2003, vol. 116, issue 3, No 4, 558 pages

Abstract: Abstract In this paper, the H 2/H ∞ problem is considered in a transfer-function setting, i.e., without a priori chosen bounds on the controller order. An optimization procedure is described which is based on a parametrization of all feasible descending directions stemming from a given point of the feasible transfer-function set. A search direction at each such point can be obtained on the basis of the solution of a convex finite-dimensional problem which can be converted into a LMI problem. Moving along the chosen direction in each step, the procedure in question generates a sequence of feasible points whose cost functional values converge to the optimal value of the H 2/H ∞ problem. Moreover, this sequence of feasible points is shown to converge in the sense of a weighted H 2 norm; and it does so to the solution of the H 2/H ∞ problem whenever such a solution exists.

Keywords: H 2/H ∞ optimal control; linear control systems (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1023013302934

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