Control Synthesis for Hypersonic Vehicle Flight Testing with Input-Output-Sampled Nonlinearities

The flight testing of hypersonic vehicles is challenging due to the nonlinear, uncertain, and possibly unstable dynamics of these vehicles. This paper presents a control synthesis method for a hypersonic vehicle with the purpose of guaranteeing robust stability during flight testing when accurate analytic vehicle models are unavailable. Conventional model-based approaches typically rely on curve fitting of numerical simulation and test data, which can introduce inaccuracies. Our proposed approach assumes knowledge of the linear form of the ordinary differential equation and uses quadratic constraints to bound sampled data that accounts for the nonlinear and uncertain portion of the model for controller synthesis by iteratively solving convex semidefinite programs. A numerical example demonstrating the effectiveness of the proposed method is performed before applying the technique to a nonlinear hypersonic vehicle found in the literature. Using the synthesized stabilizing controller, we demonstrate that the vehicle states remain within a certified bound given a known harmonic excitation when initiated from a quantified set of allowable initial conditions. Based on these simulation results, our proposed control synthesis method shows promise in ensuring robustness when performing hypersonic vehicle flight testing.