This paper describes an algorithm for a general minimum fuel control problem. The objective function of the problem is represented by the functional: F~0 (x, u) = F~(0,1) (x, u) + F~(0,2) (x, u) where F~(0,1) is continuously differentiable with respect to states x and controls u, while F~(0,2) includes the term integral_0~(t_f) sum_(i=1)~m g_i(t, x(t))|u_i(t) -u_i~r(t)| dt. A direction of descent of the algorithm is found by solving a convex (possibly non-differentiable) optimization problem. An efficient version of a proximity algorithm is used to solve this sub-problem. State and terminal constraints are treated via a feasible directions approach and an exact penalty function respectively. The algorithm is globally convergent under minimal assumptions imposed on the problem. Every accumulation point of a sequence generated by the algorithm satisfies the combined strong-weak version of the maximum principle condition.
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