Control Synthesis for a Hypersonic Vehicle with Harmonic Excitation Inputs and Input-Output-Sampled Nonlinearities

This paper presents a control synthesis method for the flight testing of a hypersonic vehicle. The dynamic model of a hypersonic vehicle is highly nonlinear and features terms that are the result of computational fluid dynamics simulations or data from wind tunnel testing performed across a number of operating conditions. This results in lookup-table-based models that are not analytic in nature, making it difficult to apply typical nonlinear control techniques without curve fitting, which can introduce inaccuracies. To overcome the need for curve fitting, the proposed control synthesis method uses quadratic constraints to bound the sampled nonlinear dynamics of a hypersonic vehicle for control synthesis. Sampling the nonlinear dynamics comes with the challenge of synthesizing a controller while staying within the bounds of the sampled region. This is addressed in the proposed approach through an iterative synthesis method that involves solving convex semi-definite programs. Flight tests often include harmonic inputs to excite the vehicle’s dynamics for system identification and refinement purposes. A novel feature of the proposed control synthesis method is the ability to bound the vehicle’s states in the presence of these harmonic excitation signals. This provides a quantification of the region of allowable initial conditions that will ensure the vehicle stays within the sampled region of the state space, as demonstrated in numerical simulation results.