Free‐Final‐Time Sensitivity‐Based Pseudospectral Guidance Algorithm for Terminal Speed Maximization Under Input Constraints

ABSTRACT This paper proposes a free‐final‐time sensitivity‐based pseudospectral constrained guidance algorithm for terminal‐speed maximization under control input constraints. Within a free‐final‐time formulation, the sensitivity relationships of terminal outputs with respect to both control updates and final‐time variations are explicitly established, allowing the final time and control history to be optimized in a coupled manner. This treatment enlarges the solution space under multiple constraints and enables direct terminal‐speed optimization without auxiliary variables or indirect performance measures. By adopting a quasi‐spectral representation, the control input is parameterized using a finite set of basis functions, transforming the original infinite‐dimensional continuous‐time optimization formulation into a low‐dimensional static programming problem and yielding a computationally efficient suboptimal solution. A violation‐activated penalty mechanism is incorporated to efficiently handle acceleration constraints without reliance on external solvers. Furthermore, flipped Radau pseudospectral discretization is employed to enhance efficiency in sensitivity matrix calculation. Numerical simulations demonstrate that the proposed guidance algorithm achieves higher terminal speed while satisfying multiple constraints and exhibits superior computational efficiency compared with existing guidance algorithms.