Multi-objective H₂/H∞/Impulse-to-Peak Control of a Space Launch Vehicle

A multi-objective synthesis problem involving H₂, H∞ and impulse-to-peak performances is investigated. In general, multi-objective control problems are hard problems to solve and do not have exact solutions. Here, an LMI formulation is proposed for the mixed H₂/impulse-to-peak optimization under an H∞ constraint for LTI discrete-time systems. This framework is then used to control the attitude of a space launcher. A particular control structure is defined and a multi objective H₂=H∞/impulse-to-peak synthesis problem is solved to tackle specific specifications. A systematic synthesis procedure including the tuning of design parameters is defined and results from simulations are presented.