Abstract:
For a general optimal control problem with state and regular mixed constraints we propose a proof of the maximum principle based on the so-called $v$-change of time variable $t \mapsto \tau$, under which the original time becomes an additional state variable subject to the equation $dt/d\tau = v(\tau)$, while the additional control variable $v(\tau)\geqslant 0$ is piecewise constant, and its values become arguments of the new problem.
Keywords:state and mixed constraints, positively linearly independent vectors,
$v$-change of time, Lebesgue–Stieltjes measure, stationarity conditions, Lagrange multipliers,
functional on $L_\infty$, weak* compactness, maximum principle.
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