Examples of nonclassical feedback control problems

Alberto Bressan; Deling Wei

doi:10.1007/s00030-012-0165-2

Examples of nonclassical feedback control problems

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Abstract

We consider a control system with "nonclassical" dynamics: ẋ = f(t, x, u, D_xu), where the right hand side depends also on the first order partial derivatives of the feedback control function. Given a probability distribution on the initial data, we seek a feedback u = u(t, x) which minimizes the expected value of a cost functional. Various relaxed formulations of this problem are introduced. In particular, three specific examples are studied, showing the equivalence or non-equivalence of these approximations.

Original language	English (US)
Pages (from-to)	249-271
Number of pages	23
Journal	Nonlinear Differential Equations and Applications
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/s00030-012-0165-2
State	Published - Apr 2013

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s00030-012-0165-2

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author = "Alberto Bressan and Deling Wei",

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AB - We consider a control system with "nonclassical" dynamics: ẋ = f(t, x, u, Dxu), where the right hand side depends also on the first order partial derivatives of the feedback control function. Given a probability distribution on the initial data, we seek a feedback u = u(t, x) which minimizes the expected value of a cost functional. Various relaxed formulations of this problem are introduced. In particular, three specific examples are studied, showing the equivalence or non-equivalence of these approximations.

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Examples of nonclassical feedback control problems

Abstract

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