Optimal Control of Linear Stochastic Systems With Quadratic Criterion Under Classical Information Structure
Kenko Uchida, Etsujiro SHIMEMURA · Transactions of the Society of Instrument and Control Engineers · 1976
In this paper optimal control problems of linear stochastic systems with a quadratic criterion under a classical information structure are discussed. The emphasis is put on an effort to derive the condition under which the certainty equivalence property holds, and it is shown the most essential sufficient conditions are (I) that the system is linear, (II) that the performance criterion is quadratic and (III) that the information structure is classical. These conditions do not require any assumption on the statistical property of noise processes and an initial state. That is, even if the additive noise processes are arbitrary stochastic processes and the initial state is an arbitrary stochastic variable, the certainty equivalence property holds under the conditions (I), (II) and (III). Next, filtering problems are discussed. In the case where the noise process of dynamics and the initial state are nongaussian, the Kalman-Bucy like filter is derived. Problems are formulated and discussed with the continuous time model. To clarify the sufficiency of the conditions (I), (II) and (III), the discrete time case is also discussed.