Envelopes , Higher - Order Optimality Conditions , and Lie
نویسنده
چکیده
We describe a generalization to Optimal Control of the theory of envelopes of the classical Calculus of Variations. This generalization extends our previous work, by allowing the use of \quasi-extremal" trajectories, i.e. trajectories that satisfy all the conditions of the Pontryagin Maximum Principle except for the fact that the sign of the constant 0 that appears in the Hamiltonian multiplying the Lagrangian is not restricted, and by making it possible to prove nonoptimality of some \abnormal" trajectories. We illustrate the use of the envelope technique by presenting an alternative proof of a theorem of Agrachev, Gamkrelidze and Schh attler on the number of switchings of time-optimal bang-bang trajec-tories for two-vector-eld systems in three dimensions.
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