A novel adaptive Gauss pseudospectral method for nonlinear optimal control of constrained hypersonic re-entry vehicle problem

Optimal control of constrained hypersonic re-entry vehicle is difficult due to the complex nonlinear dynamics and nonlinear constraints. A novel adaptive Gauss pseudospectral method with some new strategies is therefore proposed to deal with the optimal control problem of hypersonic re-entry vehicle to ensure that the complex constraints are satisfied all the way. First, state transformation is applied to make the variables more uniform in quantities. Second, some extreme points are applied in designing appropriate subintervals to track the control profiles effectively and the collocation points are adaptively redistributed based on the evaluated approximation errors. Third, a detection procedure is proposed to ensure that the constraints are satisfied all the way during the whole re-entry process. The proposed method is illustrated by testing a hypersonic re-entry vehicle problem. The results reveal that path constraints and terminal conditions are well satisfied. The research results, including the comparison with other methods, such as the classical Gauss pseudospectral method and the control vector parameterization method, show the effectiveness of the proposed adaptive approach.