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In this paper we investigate the problem of controlling a partially observedstochastic dynamical system such that its state is difficult to infer using a(fixed-interval) Bayesian smoother. This problem arises naturally inapplications in which it is desirable to keep the entire state trajectory of asystem concealed. We pose our smoothing-averse control problem as the problemof maximising the (joint) entropy of smoother state estimates (i.e., the jointconditional entropy of the state trajectory given the history of measurementsand controls). We show that the entropy of Bayesian smoother estimates forgeneral nonlinear state-space models can be expressed as the sum of entropiesof marginal state estimates given by Bayesian filters. This novel additive formallows us to reformulate the smoothing-averse control problem as a fullyobserved stochastic optimal control problem in terms of the usual concept ofthe information (or belief) state, and solve the resulting problem via dynamicprogramming. We illustrate the applicability of smoothing-averse control toprivacy in cloud-based control and covert robotic navigation.

Smoothing-Averse Control: Covertness and Privacy from Smoothers