The focus of this paper is on the design of shaped profiles subject to transient state constraints and terminal energy limits. The issue of robustness to modeling errors is addressed by formulating a minimax optimization problem in a linear programming framework, permitting the generation of near-globally optimal shaped profiles. To illustrate the proposed technique, a deflection-limited/residual energy constrained, controller design for flexible structures undergoing rest-to-rest maneuvers will be presented. Techniques for improving robustness by the addition of state sensitivity equations, which increases the robustness in the vicinity of the nominal model, are explored. Results for the benchmark oscillator illustrate the benefit of the proposed approach over traditional designs.