The bang–bang theorem via Baire category: a dual approach

Alberto Bressan; Marco Mazzola; Khai T. Nguyen

doi:10.1007/s00030-016-0400-3

The bang–bang theorem via Baire category: a dual approach

Alberto Bressan
, Marco Mazzola
, Khai T. Nguyen

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The paper develops a new approach to the classical bang–bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point x¯ , we consider those which minimize an auxiliary linear functional ϕ. For all ϕ in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.

Original language	English (US)
Article number	46
Journal	Nonlinear Differential Equations and Applications
Volume	23
Issue number	4
DOIs	https://doi.org/10.1007/s00030-016-0400-3
State	Published - Aug 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s00030-016-0400-3

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abstract = "The paper develops a new approach to the classical bang–bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point x¯ , we consider those which minimize an auxiliary linear functional ϕ. For all ϕ in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.",

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AB - The paper develops a new approach to the classical bang–bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point x¯ , we consider those which minimize an auxiliary linear functional ϕ. For all ϕ in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.

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The bang–bang theorem via Baire category: a dual approach

Abstract

All Science Journal Classification (ASJC) codes

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