Occupational Measures Formulation and Linear Programming Solution of Deterministic Long Run Average Problems of Optimal Control

Gaitsgory, Vladimir; Rossomakhine, Sergey

doi:10.1109/cdc.2006.377568

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2023

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“…References 8,9,10,11 consider an optimal control problem "in the long run", that is, with slow and "normal" time scales, using averaging techniques. The convergence of the optimal cost is proved, but there is no estimation of the loss of optimality that the approximation method produces.…”

Section: Historical Perspectivementioning

confidence: 99%

Empirical averaging in deterministic optimal control

Chaplais

Bernard

2023

Preprint

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A windowed averaged scheme is defined for general control systems. The same method is used to average costs in optimal control problems (OCPs). A numerical parameter α can be computed, which expresses the distance between the original system and the averaged system in a weak sense. The value of α is well defined for any system. Then, if we use the optimal control of the averaged OCP in the original OCP, the suboptimality of the control is bounded by an expression of the form C α 2 . This bound holds for any optimal control problem which satisfies the Legendre-Clebsch condition and such that the convexity parameter satifies a general inequation with respect to the numerical parameter α.

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Section: Historical Perspectivementioning

confidence: 99%