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

Abstract

SummaryOptimal 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.

Time-varying Formation Dynamics Modeling and Constrained Trajectory Optimization of Multi-quadrotor UAVs

“…The terminal state is obtained from the initial state and the integral of the right function, and Gauss integral is used for discretization calculation. After the above transformation, the original optimal control problem is transformed into a parametric optimization problem with a series of algebraic constraints, which is also called Nonlinear Programming problem (NLP) [35][36][37].…”

An improved adaptive hp mesh refinement method in solving optimal control problems

“…In recent years, many scholars have carried out extensive research on it and greatly developed its related theory and application [26][27][28][29][30]. Li et al [31,32] apply the adaptive hp method to the field of trajectory optimization, which effectively solve this kind of complex nonlinear optimization problem, and obtain satisfactory solution accuracy. By improving the mesh refinement process, some effective variants of the hp method are proposed in [33][34][35][36][37].…”

An Improved Adaptive hp Mesh Refinement Method in Solving Optimal Control Problems

“…In recent years, many scholars have carried out extensive research on it and greatly developed its related theory and application [26][27][28][29][30]. Li et al [31,32] apply the adaptive hp method to the field of trajectory optimization, which effectively solve this kind of complex nonlinear optimization problem, and obtain satisfactory solution accuracy. By improving the mesh refinement process, some effective variants of the hp method are proposed in [33][34][35][36][37].…”

“…Although the aforementioned works [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] on the adaptive hp method has made great progress, there still are several issues that need further consideration.…”