In this paper, tube-model predictive control based on the sum of squares technique is developed for hypersonic vehicles with state-dependent input constraints. Firstly, the longitudinal non-linear model in the presence of uncertain parameters is transformed into the polytopic linear parameter varying model with bounded disturbance by feedback linearization. Then the actual input constraints are converted to the virtual state-dependent input constraints in linear multivariable polynomial. A composite feedback control law based on tube-model predictive control is designed into a convex combination of unconstrained and constrained control. The real control law can be obtained by inversion. The sum of squares technique is used to transform the polynomial constraints into the convex matrix sum of squares condition via linear matrix inequality. Finally, simulation results verify the effectiveness of the proposed controller.
Approximate Model Predictive Control for Nonlinear Multivariable Systems
