Abstract: This paper proposes a real time trajectory optimization method based on the Proximal Newton Kantorovich convex programming for the energy management of a solid rocket in atmosphere. In order to solve the problem that traditional energy management method is difficult to strictly satisfy the atmospheric process constraints, a regularization method is proposed first to punish the modular integral of control variables, transforming the energy management problem to the trajectory optimization problem. Then, for the strong nonlinear dynamics and constraints in the atmosphere, a Proximal Newton Kantorovich convex programming method is proposed, which linearizes the nonlinear term in the optimization problem and introduces the proximal term in the performance index to improve the convergence of the algorithm. Finally, the virtual control variables are introduced to relax the control constraints and process constraints to reduce the dependence of the optimization algorithm on the initial guess. The mathematical simulation shows that the proposed trajectory optimization method is effective to solve the energy management problem, which can strictly satisfy the constraints and achieve high accuracy terminal. In addition, the algorithm has good real time performance, which can meet the requirements of energy management for calculating speed.

Key words: Solid rocket energy management, Atmospheric ascent phase, Trajectory optimization, Convex programming