An algorithm for a minimum fuel control problem

This paper describes an algorithm for a general minimum fuel control proble m. The objective function of the problem is represented by the functional: F-0(x, u) - F-0,F-1(x, u) + F-0,F-2(x, u) where F-0,F-1 is continuously dif ferentiable with respect to states x and controls u, while F-0,F-2 includes the term integral(0)(1f) Sigma(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 (pos sibly non-differentiable) optimization problem. An efficient version of a p roximity algorithm is used to solve this sub-problem. State and terminal co nstraints are treated via a feasible directions approach and an exact penal ty function respectively. The algorithm is globally convergent under minima l assumptions imposed on the problem. Every accumulation point of a sequenc e generated by the algorithm satisfies the combined strong-weak version of the maximum principle condition.