A downgraded Trajectory Optimization Method Combining Deep Neural Networks and Lossless Convex Optimization for Thrust Descent Failure

In order to enable the launch vehicle to use the remaining fuel as much as possible to inject the optimal degraded orbit in the event of thrust descent failure which prevents the rocket from completing its original mission, three orbit degradation strategies are proposed. The corresponding terminal orbits for these three strategies are (1) A circular orbits with maximum energy; (2) An elliptical orbit with maximum energy constrained by perigee and apogee heights; (3) An Elliptical orbit with minimum eccentricity. A pseudo-spectral sequence convex optimization method is adopted to solve the optimal control problem corresponding to these three strategies. In order to ensure the convergence of the algorithm, non-convex terminal constraints and objective functions are convexified by lossless convexity instead of simple linearization, including equivalent transformation and relaxation of constraints based on flight dynamics, as well as introducing the additional coasting phase. But the above operation will introduce new variables to be optimized, including the perigee angle and the coasting time, which will generate additional non-convex terms. A two-layer algorithm (TLA) was adopted for this difficulty: using a sequential second-order cone programming method to solve the optimization problem under fixed perigee angles in the inner layer and using the Newton's method to solve the optimization problem of perigee angle in the outer layer. In order to further ensure the convergence of the algorithm and improve computational efficiency, a fusion algorithm (FA) combining lossless convexification and deep neural networks (DNNs) is proposed, which utilizes DNNs to generate the coordinate rotation angles required for inner optimization online. This indirect application of artificial intelligence can significantly reduce the application risk while improving the performance of traditional optimization algorithms. Numerical simulations are conducted to compare the proposed FA and existing linearization algorithms + DNNs in different fault scenarios, which show that the proposed method has stronger convergence and higher engineering value.