Adaptive Generalized Quasi-Spectral Model Predictive Convex Programming for Constrained Guidance

This article presents an adaptive generalized quasi-spectral model predictive convex programming (AGS-MPCP) framework for constrained guidance problems based on Gaussian orthogonal collocation. The approach formulates a constrained MPCP scheme in which the state and control trajectories are represented by a finite set of spectral coefficients rather than by node-based discretization, thereby enabling an adaptive collocation mechanism within a convex-optimization framework. This spectral parameterization substantially reduces the dimensionality of the optimization problem, while all path and terminal constraints are reformulated as equality and inequality matrix equations within a convex programming structure, enabling flexible cost-function design for improved optimal-control performance. An adaptive collocation strategy selectively incorporates local extrema of state and control constraint profiles into the inequality-constraint set, and adjusts the collocation density according to the integration interval length, thereby preventing oversampling in short segments and ensuring adequate resolution over long horizons. Numerical simulations on long-duration aerospace trajectory optimization scenarios demonstrate that AGS-MPCP achieves high terminal accuracy, fast convergence, and superior computational efficiency compared with existing constrained MPCP and model predictive static programming variants. Monte Carlo evaluations further verify its robustness to parameter uncertainties and initial-condition perturbations, indicating its suitability for high-fidelity, constraint-compliant guidance in complex mission environments.