Multi-objective and reliable control for trajectory-tracking of rendezvous via parameter-dependent Lyapunov functions

A reliable, multi-objective and state-feedback controller design algorithm is presented for trajectory-tracking of circular-orbit rendezvous, in which H∞ performance, H∞ performance and regional pole placement are taken into account. Given actuator failures and exogenous disturbances, the dynamical model is described as a polytopic system. By applying parameter-dependent Lyapunov functions and introducing slack matrices, the condition for the existence of multi-objective controller is described as a non-convex optimization subject to nonlinear matrix inequality constraints. Then, a hybrid genetic algorithm is proposed to obtain the desired controller. Numerical simulations are given to show that the proposed method can (a) handle actuator failures and exogenous disturbances effectively, and (b) provide better disturbance-attenuation performances than conventional methods.