Design of Optimal Controls in Acausal LQG Problems

In control theory, a system which has output depending only on the present and past values of the input is said to be causal (or nonanticipative). Respectively, a system is acausal (or non-causal) if its output depends on future inputs as well. Overall majority of literature in stochastic control theory discusses causal systems. Only a few sources indirectly concern acausal systems. In this paper, we systemize these results under main idea of acausality and present a background for designing optimal controls in acausal LQG problems.