Event-triggered risk-sensitive smoothing for linear Gaussian systems

An event-triggered risk-sensitive smoothing problem for linear Gaussian systems is investigated in this paper. Due to the special cost criterion of the risk-sensitive estimation, the smoothed information state is first constructed under a newly defined reference measure. Its Gaussian density and recursive forms are derived by processing it into the combination of the forward and backward information states, both of which are proven to have Gaussian densities and evolve in linear recursions. A stochastic even-triggering condition is adopted to preserve the Gaussian property during the derivation. Then the proposed problem is reformulated equivalently under the reference measure, expressed by minimizing an integral involving the smoothed information state, and finally solved by utilizing the Gaussian densities of information states. The applicability and effectiveness of the results are illustrated through a numerical example by comparisons with a naive risk-sensitive smoother and the event-triggered MMSE smoother.