Bang-Bang Controls and Their Relation to Regularity and Normality Conditions
نویسندگان
چکیده
منابع مشابه
Second Order Optimality Conditions for Controls with Continuous and Bang-Bang Components
Second order necessary and sufficient optimality conditions for bang-bang control problems in a very general form have been obtained in Milyutin and Osmolovskii (1998). These conditions require the positive (semi)-definiteness of a certain quadratic form on the finite-dimensional critical cone. Using a suitable transformation via a linear matrix ODE, Maurer and Osmolovskii (2003, 2004) have dev...
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We study bang–bang control problems that depend on a parameter p. For a fixed nominal parameter p0, it is assumed that the bang-bang control has finitely many switching points and satisfies second order sufficient conditions (SSC). SSC are formulated and checked in terms of an associated finitedimensional optimization problem w.r.t. the switching points and the free final time. We show that the...
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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.
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A large collection of financial contracts offering guaranteed minimum benefits are often posed as control prob4 lems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of 5 values from the admissible set. Often, such contracts specify that the holder exerts control at a finite number of 6 deterministic times. The existence of an optimal ban...
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We provide sufficient optimality conditions for optimal control problems with bang-bang controls. Building on a structural assumption on the adjoint state, we additionally need a weak second-order condition. This second-order condition is formulated with functions from an extended critical cone, and it is equivalent to a formulation posed on measures supported on the set where the adjoint state...
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ژورنال
عنوان ژورنال: Transactions of the Society of Instrument and Control Engineers
سال: 1971
ISSN: 0453-4654
DOI: 10.9746/sicetr1965.7.401