Convex optimization is of great interest as an efficient and reliable solver in the field of aerospace engineering. Existing research often focuses on developing proper convexification techniques to handle aerospace problems within the convex optimization framework, with limited attention to further efficiency enhancements in convex optimization solving, such as by reducing the optimization problem size. Motivated by the real-time requirements of onboard aerospace applications, this paper presents a unified framework for reduced space sequential convex programming formulations, emphasizing a significant reduction of optimization variables and constraints. The primary idea is to employ an iterative scheme to explicitly approximate the dynamic implicit function and subsequently eliminate the explicitly defined state variables and dynamic equality constraints, thereby constructing a sequence of reduced space optimization subproblems to be solved iteratively. Within the proposed framework, a family of reduced space sequential convex programming methods with different performance-complexity tradeoffs are developed by virtue of the fixed-point iteration, Newton iteration, damped Newton iteration, and simplified Newton iteration. Numerical simulations for a minimum-fuel rocket landing problem inside atmosphere are conducted to demonstrate the performance of the developed methods.

This paper presents a feasible sequential convex programming method to solve the multistage ascent trajectory optimization problem. The proposed method is based on the inexact restoration technique, in which a more feasible intermediate iterate is first produced by solving a constrained least-squares problem, and then a more optimal iterate is generated by solving a convex programming problem constructed around the newly found feasible solution. By virtue of the inexact restoration idea, the proposed method prevents the common artificial infeasibility issue and can provide the intermediate iterate as a feasible suboptimal solution if the algorithmic procedure terminates before convergence. In addition, the Picard iteration-based convexification and Chebyshev polynomial-based discretization methods are employed in the proposed method, given their benefits in terms of robustness, efficiency, and solution accuracy. Numerical simulations for a minimum-time launch ascent problem are conducted, and the results show that the proposed method exhibits better practical performance than other sequential convex programming methods.

Inspired by the widely used smoothing techniques in image processing and statistical analysis, a novel smoothing homotopy paradigm is proposed in this paper for solving general optimal control problems with the indirect method. In contrast to the existing approaches, the sensitivity associated with the two-point-boundary-value problem (TPBVP) in optimal control is reduced by convoluting appropriate part of the TPBVP with a smoothing kernel. The homotopic process is applied to the bandwidth of the smoothing: a larger bandwidth produces a stronger smoothing effect, rendering the TPBVP better behaved and much easier to solve; a zero bandwidth results in no smoothing and thus leads to the original TPBVP. Depending on whether the Gaussian smoothing kernel or a non-Gaussian kernel is used in the particular implementation, two different smoothing homotopy methods are developed, each with distinctive features of its own. Challenging numerical examples are provided to demonstrate the working and effectiveness of the methods.