Abstract
An optimal guidance algorithm for air-breathing launch vehicle is proposed based on optimal trajectory correction. The optimal trajectory correction problem is a nonlinear optimal feedback control problem with state inequality constraints which results in a nonlinear and nondifferentiable two-point boundary value problem (TPBVP). It is difficult to solve TPBVP on-board. To reduce the on-board calculation cost, the proposed guidance algorithm corrects the reference trajectory in every guidance cycle to satisfy the optimality condition of the optimal feedback control problem. By linearizing the optimality condition, the linear TPBVP is obtained for the optimal trajectory correction. The solution of the linear TPBVP is obtained by solving linear equations through the Simpson rule. Considering the solution of the linear TPBVP as the searching direction for the correction values, the updating step size is generated by linear search. Smooth approximation is applied to the inequality constraints for the nondifferentiable Hamiltonian. The sufficient condition for the global convergence of the algorithm is given in this paper. Finally, simulation results show the effectiveness of the proposed algorithm.
Highlights
The development of space technology has given rise to the expectation that launchers will become low cost and fully reusable
We present an optimal guidance algorithm for air breathing launch vehicle based on optimal trajectory correction to reduce the on-board calculation cost
For the real-time requirement of the on-board algorithm, the linear two-point boundary value problem (TPBVP) is obtained for optimal trajectory correction by linearizing the optimality condition in this paper
Summary
The development of space technology has given rise to the expectation that launchers will become low cost and fully reusable. An adaptive guidance law and off-board trajectory optimization for air-breathing launch vehicle were addressed in [22]. The indirect method was implemented for ascent trajectory optimization on-board considering the features of the air-breathing vehicle. We present an optimal guidance algorithm for air breathing launch vehicle based on optimal trajectory correction to reduce the on-board calculation cost. Considering the current vehicle state as the initial condition, the optimal trajectory correction problem is referred to as a nonlinear optimal control problem with state inequality constraints. For the real-time requirement of the on-board algorithm, the linear TPBVP is obtained for optimal trajectory correction by linearizing the optimality condition in this paper.
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