  In this paper we investigate the problem of controlling a partially observed
stochastic dynamical system such that its state is difficult to infer using a
(fixed-interval) Bayesian smoother. This problem arises naturally in
applications in which it is desirable to keep the entire state trajectory of a
system concealed. We pose our smoothing-averse control problem as the problem
of maximising the (joint) entropy of smoother state estimates (i.e., the joint
conditional entropy of the state trajectory given the history of measurements
and controls). We show that the entropy of Bayesian smoother estimates for
general nonlinear state-space models can be expressed as the sum of entropies
of marginal state estimates given by Bayesian filters. This novel additive form
allows us to reformulate the smoothing-averse control problem as a fully
observed stochastic optimal control problem in terms of the usual concept of
the information (or belief) state, and solve the resulting problem via dynamic
programming. We illustrate the applicability of smoothing-averse control to
privacy in cloud-based control and covert robotic navigation.
