Bang-bang optimality of energy efficient spikes in single neuron models
نویسندگان
چکیده
منابع مشابه
Strong Optimality for a Bang-Bang Trajectory
In this paper we give sufficient conditions for a bang-bang regular extremal to be a strong local optimum for a control problem in the Mayer form; strong means that we consider the C0 topology in the state space. The controls appear linearly and take values in a polyhedron, and the state space and the end point constraints are finite-dimensional smooth manifolds. In the case of bang-bang extrem...
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where ƒ and g are smooth vector fields. Admissible controls are arbitrary measurable functions with values in [—1,4-1] and a trajectory of the system corresponding to a control u( ) is an absolutely continuous curve such that x(t) — f{x(t)) + u(t)g(x(t)) holds almost everywhere. In every optimal control problem the question of regularity of the solutions comes up naturally. The standard existen...
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Second order necessary and sufficient optimality conditions for bang–bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi–)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadr...
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Abstract: In this paper we study optimal control problems with bang-bang solution behavior for a special class of semilinear dynamics. Generalizing a former result for linear systems, optimality conditions are derived by a duality based approach. The results apply for scalar as well as for vector control functions and, in particular, for the case of the so-called multiple switches, too. Further...
متن کاملStrong Local Optimality for a Bang-Bang Trajectory in a Mayer Problem
This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in [5, 13] and [16]. We require both the strict bang-bang Legendre condition, and the second order conditions for the finite dimensional problem obtained by moving the switching times ...
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ژورنال
عنوان ژورنال: Frontiers in Neuroscience
سال: 2010
ISSN: 1662-453X
DOI: 10.3389/conf.fnins.2010.03.00085