TY - JOUR

T1 - Non-classical problems of optimal feedback control

AU - Bressan, Alberto

AU - Wei, Deling

N1 - Funding Information:
This research was partially supported by NSF, with grant DMS-1108702: “Problems of Nonlinear Control”.

PY - 2012/8/15

Y1 - 2012/8/15

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jde.2012.04.020

DO - 10.1016/j.jde.2012.04.020

M3 - Article

AN - SCOPUS:84861481924

SN - 0022-0396

VL - 253

SP - 1111

EP - 1142

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -