Max-Max type entry trajectory optimization for testing vehicle by successive difference-of-convex programming

Employing the DC (difference-of-convex) programming method, a study is conducted on the extreme performance of the testing entry vehicle in terms of peak heat flux.

Successive DC programming method; big-M method; mixed-integer nonlinear programming

Numerical examples show that the DC relaxation based model has higher approximation accuracy for Max-Max type entry trajectory optimization problems than the linearization based model, and performs better in numerical stability, convergence characteristics, and optimality. It is suitable for high-precision entry heat trajectory planning tasks and can provide reference for vehicle heat testing. Due to the addition of more linear and nonlinear constraints to DC relaxation based model, the speed of solving DC relaxation based model is significantly slower than solving the linearization based model.

To evaluate the force and heat performance of entry vehicles and provide testing references for material, aerodynamic, and structural design departments, this paper uses the successive DC programming method to study a Max-Max type entry trajectory optimization problems. The main contribution of this article lies in: (1) Combining DC decomposition and penalty function method to derive a Max-Max type cost function DC relaxation model with higher approximation accuracy than the linearized model, which solves the problem of cost function oscillation or non-convergence during the iteration process of the linearized model; (2) The Max-Max type trajectory optimization problem is transformed into a solvable mixed integer programming subproblem employing the Big-M method, and an improved successive DC programming method based on the DC relaxation model is proposed. Taking the optimization problem of peak heat flux entry trajectory as the research object, numerical experiments show that the maximum peak heat flux trajectory optimization method based on DC relaxation model is 0.5781% higher in optimality than the linearization model method, and the terminal latitude and longitude accuracy is 2 orders of magnitude higher. The proposed method has high stability, convergence, and optimality.