Non-classical problems of optimal feedback control

Alberto Bressan, Deling Wei

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The paper is concerned with problems of optimal feedback control with "non-classical" dynamics ẋ=f(t,x,u,Du), where the evolution of the state x depends also on the Jacobian matrix Du=(∂u i/∂x j) of the feedback control function u=u(t, x). Given a probability measure μ on the set of initial states, we seek feedback controls u({dot operator}) which minimize the expected value of a cost functional. After introducing a basic framework for the study of these problems, this paper focuses on three main issues: (i) necessary conditions for optimality, (ii) equivalence with a relaxed feedback control problem in standard form, and (iii) dependence of the expected minimum cost on the probability measure μ.

Original languageEnglish (US)
Pages (from-to)1111-1142
Number of pages32
JournalJournal of Differential Equations
Issue number4
StatePublished - Aug 15 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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