Online Tube-MPC via substitute observation for flexible hypersonic vehicle with time-varying input delay

In this paper, a novel online tube model predictive control (Tube-MPC) method is proposed for flexible hypersonic vehicle with time-varying input delay. The polytopic linear parameter varying (LPV) model with time-varying input delay is established and further transformed into a polytopic LPV delay-free model by input delay model transformation (IDMT). Since the flexible states cannot be measured accurately due to vehicle body deformation, the polytopic Luenberger observer is developed. To reduce control conservatism, substitute observations are used to replace the actually observed states such that the new reduced control error invariant set (CEI) is generated. On the basis, the Tube-MPC controller is designed, where the offline robust feedback control law and the online nominal control law are devised via linear matrix inequality (LMI) separately. For figuring out the invariant set of nominal control, an offline-online synthesized method is proposed by combining interpolation-based offline computation (IOFC) with substitute observation-based online computation (SOOC). In IOFC, the sequences of observation error invariant set (OEI) and CEI are computed offline iteratively and further interpolated so as to reduce online computation burden. The online judgement and update mechanism is proposed in SOOC. When the observed states enter the expanded invariant set constructed by the interpolated OEI and CEI, the substitute observation-based control error invariant set (SOCEI) will be calculated online and accordingly the nominal control law can also be updated. The simulation results verify the proposed control method’s effectiveness for flexible hypersonic vehicle with time-varying input delay.