an:04062980
Zbl 0651.93078
Nakano, Kazushi; Sagara, Setsuo
Optimal scanning measurement problem for a stochastic distributed- parameter system
EN
Int. J. Syst. Sci. 19, No. 7, 1069-1083 (1988).
00167981
1988
j
93E20 93C20 93E10 49J55
.; maximum principle; stochastic control problem; non-smooth drift; adjoint process; optimal measurement scheduling; stochastic distributed- parameter system; continuous and discrete scanning observations; N-modal approximation; relaxed controls; approximate solution
A maximum principle for a stochastic control problem \(dx_ t=f(t,x_ t,u_ t)dt+\sigma (t,x_ t)dB_ t\), \(x(0)=x\), \(J(u)=E_ x[g(x_ T)]\), with non-smooth drift is established by approximating this problem by differentiable problems. In this way Kushner's maximum principle is generalized and the adjoint process is characterized. The authors deal with the problem of determining the optimal measurement scheduling for a stochastic distributed-parameter system based on spatially continuous and discrete scanning observations. For the continuous scanning case the authors prove the existence of optimal solutions and establish the N- modal approximation problem. For the discrete case the authors introduce the concept of relaxed controls and present a practical method of constructing an approximate solution for the relaxed problem. Finally, the authors give a numerical example to compare two types of optimal measurement trajectory.
M.Kohlmann S.Sun