Non-classical problems of optimal feedback control

作者：Bressan Alberto^*; Wei Deling

来源：Journal of Differential Equations, 2012, 253(4): 1111-1142.

DOI：10.1016/j.jde.2012.04.020

The paper is concerned with problems of optimal feedback control with "non-classical" dynamics x(over dot) = f (t, x, u, Du), where the evolution of the state x depends also on the Jacobian matrix Du = (partial derivative u(i)/partial derivative x(j)) of the feedback control function u = u(t, x). Given a probability measure mu on the set of initial states, we seek feedback controls mu(.) 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 mu.

• 出版日期2012-8-15