Receding Horizon Optimal controller for reference trajectory tracking in Mars entry guidance

In the process of the high-speed vehicle sentering a rarefied atmosphere with highly uncertainties as the Mars atmosphere, the trajectory deviation caused by entry guidance can be the major part of the total landing errors. To reduce the impact of model errors on guidance performance, a guidance law based on receding horizon control is developed for reference trajectory tracking. At each guidance cycle, the prescribed trajectory as well as the commanded bank angle in finite horizon is obtained by an indirect optimization method based on Pontryagin's minimum principle. Then a set of algebraic and ordinary differential equations with their boundary conditions, called boundary value problem (BVP), are obtained. In this paper, the BVP is transformed into a system of nonlinear algebraic equations by using the differential transformation method to reduce the computational burden caused by differential operation. The system of algebraic equations is solved by a trust region Newton's method. Furthermore, the closed-loop guidance law is tested by the simulation of 500 entry cases with modeling errors and compared to the feedback linearization based guidance law. Numerical simulations show that the proposed guidance scheme is feasible and effective in tracking the nominal trajectory, thus has the potential to be applied to online guidance.