Minimax defection/energy-limited controllers for flexible structures: Linear programming approach

The focus of this paper is on design of control strategies 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 controllers. 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 ameliorating robustness by the addition of state sensitivity equations which improve robustness in the vicinity of the nominal model are explored. Results for the benchmark oscillator illustrate the benefit of the proposed approach to traditional designs.