Abstract
This article presents a new result in the optimal control of a linear stochastic system with respect to a quadratic performance criterion.
It is assumed that the system is in “switching environment” as defined by Ackerson and Fu. The switching environment is expressed in terms of a stationary two state Markov chain with unknown transition probability. According to the Markov dependent switching environment, the system operates in the presence of nongaussian system noise and measurement noise which are timewise and mutually correlated, and are dependent on the nongaussian initial state.
Separability, neutrality and certainty equivalence previously proved for the so-called Linear-Quadratic-Gaussian problem are established in this stochastic optimal control problem. In this connection, a counterexample is found for the conjecture by Patchell and Jacobs that neutrality may be a sufficient condition for certainty equivalence.
