The problem of optimally controlling a class of linear stochastic systems with noisy observations and bounded controls modeled via the Girsanov transformation. The cost functional is quadratic, and the initial state is non-Gaussian and bounded. It is shown that under a certain inequaility condition for the system matrices and the weighting matrices of the cost functional, there exists a unique optimal control which is linear in the state estimate but which is nonlinear and in particular non-Lipschitzian in the observation. It is also shown that the certainly equivalence property holds.
|ジャーナル||SIAM Journal on Control and Optimization|
|出版ステータス||Published - 1983 9月|
ASJC Scopus subject areas
- 数学 (全般)