It is shown that the problem of minimizing a regulated response of a single-input/single-output system due to a fixed bounded input can be converted, via polynomial techniques, to a linear infinite-dimensional Chebyshev data fitting problem. Approximating feasible solutions within any specified degree of accuracy can be obtained by converting the original problem into a sequence of increasingly large, finite-dimensional Chebyshev approximation problems, for which solution stable and efficient numerical methods exist. A direct formula for calculating tight upper-bounds to the approximation error is provided. The link between the present algebraic approach and the Dahleh and Pearson functional analytic one is also discussed.