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In this paper, we develop a geometric analysis and a numerical algorithm, based on indirect methods, to solve optimal guidance of endoatmospheric launch vehicle systems under mixed control-state constraints. Two main difficulties are addressed. First, we tackle the presence of Euler singularities by introducing a representation of the configuration manifold in appropriate local charts. In these local coordinates, not only the problem is free from Euler singularities but also it can be recast as an optimal control problem with only pure control constraints. The second issue concerns the initialization of the shooting method. We introduce a strategy that combines indirect methods with homotopies, thus providing high accuracy. We illustrate the efficiency of our approach by numerical simulations on missile interception problems under challenging scenarios. [ABSTRACT FROM AUTHOR]

Consider the minimal time control problem for a single-input control-affine system \mathdot x=X(x) + u1 Y1 (x) in \REALR^n, where the scalar control u1(\cdot) satisfies the constraint \vert u1(\cdot )\vert \leq 1. When applying a shooting method for solving this kind of optimal control problem, one may encounter numerical problems due to the fact that the shooting function is not smooth whenever the control is bang-bang. In this article we propose the following smoothing procedure. For \varepsilon > 0 small, we consider the minimal time problem for the control system \mathdot x = X(x) + u1^{\varepsilon } Y1(x)+ \varepsilon\sum i=2^{m} ui^{\varepsilon } Yi \left (x\right), where the scalar controls ui^{\varepsilon} (\cdot), i=1,\ldots , m, with m \geq 2, satisfy the constraint \sum i=1^{m} \left (ui^{\varepsilon }(t) \right )^{2} \leq 1. We prove, under appropriate assumptions, a strong convergence result of the solution of the regularized problem to the solution of the initial problem. [ABSTRACT FROM PUBLISHER]