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3 Artstein Z.

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Pontryagin Maximum Principle for coupled slow and fast systems

Artstein Z.

Control and Cybernetics

2009

Vol. 38, no 4A

1003-1019

When slow and fast controlled dynamics are coupled, the variational limit, as the ratio of time scales grows, is best depicted as a trajectory in a probability measures space. The effective control is then an invariant measure on the fast state-control space. The paper presents the form of the Pontryagin Maximum Principle for this variational limit and examines its relation to the Maximum Principle of the perturbed system.

Bang-bang controls in the singular perturbations limit

Artstein Z.

Control and Cybernetics

2005

Vol. 34, no 3

645-663

A general form of the dynamics obtained as a limit of trajectories of singularly perturbed linear control systems is presented. The limit trajectories are described in terms of probability measure-valued maps. This allows to determine the extent to which the bang-bang principle for linear control systems is carried over to the singular limit.

Anoccupational measure solution to a singularly perturbed optimal control problem

Artstein Z.

Control and Cybernetics

2002

Vol. 31, no 3

623-642

Employing limit occupational measures, we provide an explicit solution to a singularly perturbed optimal control problem for which the order reduction method does not apply.