A variational-mechanics formulation that includes control energy in the action functional is claimed to produce optimal control laws without adjoining costate equations.
Solution of the inverse problem of the calculus of variations.Transactions of the American Mathematical Society, 50(1):71–128
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Minimum Effort Control Using Variational Methods of Analytical Mechanics A New Approach For Optimal Control
A variational-mechanics formulation that includes control energy in the action functional is claimed to produce optimal control laws without adjoining costate equations.