Optimal controller/observer gains of discounted-cost LQG systems
It solves a known gap in LQG control theory for practitioners needing optimal control with exponential discounting and state estimation.
This paper derives the optimal controller and observer gains for discounted-cost LQG systems when the state is estimated, extending previous results that only covered the known-state case. It also provides expressions for the resulting optimal expected cost.
The linear-quadratic-Gaussian (LQG) control paradigm is well-known in literature. The strategy of minimizing the cost function is available, both for the case where the state is known and where it is estimated through an observer. The situation is different when the cost function has an exponential discount factor, also known as a prescribed degree of stability. In this case, the optimal control strategy is only available when the state is known. This paper builds on from that result, deriving an optimal control strategy when working with an estimated state. Expressions for the resulting optimal expected cost are also given.