Active sensing policies for stochastic systems

In systems with sensing cost, an active sensing policy is needed to determine when to collect sensing observations. This note presents an active sensing policy for systems with additive and parametric white noise. The policy uses an open-loop estimator between sensings and a Kalman filter when observations are requested. We present two active sensing policies. The goal of the first policy is to maintain the uncertainty (variance) of the state estimate below a given threshold. Sufficient conditions are presented that guarantee that this goal is achievable and will be met. The second policy senses when needed to distinguish discrete state regions for control. Sufficient conditions are presented that show within any specified probability, the control under the active sensing will be identical to the control under conventional sensing. Experiments demonstrate that sensing and sensing communications can be significantly reduced with active sensing policies, while still meeting control objectives.