Optimal Guidance of Hypersonic Vehicles Using B-Splines and Galerkin Projection

With the advances in the computational power and numerical algorithms, recent eorts for solving the reentry problem have focused on developing a guidance system which can perform the guidance and control autonomously during the ight and in real time. In this paper, we present an algorithm in the framework of optimal control theory to guide the reentry vehicle from its entry conditions to the vicinity of the landing site, while satisfying all the path inequality constraints on dynamic pressure, heating rates and normal acceleration. The algorithm is based on formulating a nonlinear programming problem using B-Spline parameterization of the states and control trajectories. Path constraints are imposed using Galerkin’s method. The problem is setup based on X-33 vehicle model in Earth’s atmosphere. The present algorithm performs well with respect to execution time, convergence and optimality. The nal results are veried for their feasibility and optimality.

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