Enhanced Multiobjective Optimization of Aerodynamic–Control Coupling with Gramian Metrics

Optimizing supersonic vehicle aerodynamics requires integrating control performance to improve efficiency and reduce design cycles. This paper applies the concept of using the controllability Gramian matrix to enhance system controllability within the integrated design of aerodynamics and control for supersonic vehicles, developing a framework for aerodynamic–control coupling multiobjective optimization. The eigenvalues of the controllability Gramian directly quantify the impact of structural parameter variations on control energy without relying on control law design. To address the challenges of expensive multiobjective optimization, a hybrid evaluation criterion method named Kriging-Expected Improvement-Convergence Diversity Indicators (KECD) is proposed, combining an improved expected improvement with Pareto-based convergence and diversity indicators within an Non-dominated Sorting Genetic Algorithm III (NSGA-III) and kriging surrogate modeling framework. Empirical studies on Deb–Thiele–Laumanns–Zitzler (DTLZ) problems indicate that the proposed algorithm is more effective than other advanced optimization algorithms. Finally, with the optimization goals of maximizing lift and control performance while minimizing drag for the supersonic vehicle, a multiobjective optimization study on aerodynamic–control coupling is conducted. Through entropy-weighted analysis via the technique for order preference by similarity to an ideal solution, weights are assigned to the optimized Pareto front solutions. The feasibility of the coupling strategy is verified by comparing the performance of these configurations with that of the baseline configuration.