Abstract
In this paper, an l1-optimal control problem with frequency and time domain constraints on a closed-loop response is considered. The problem is formulated as an infinite dimensional linear programming problem, and the primal and dual approach is exploited. This sometimes results in non-zero gap between the primal and dual costs. This paper proposes a new method to approximate the primal and dual problems without the duality gap. As a result, the method yields a sub-optimal solution with arbitrary accuracy.
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