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The authors investigate the problem of controlling the probability density of the state of a process that is observed by the controller via a fixed but unknown function of the state. The goal is to control the process so that its probability density at a point in the state space becomes proportional to the value of the function observed at that point. Their solution, inspired by bacterial chemotaxis, involves a randomized controller that switches among different deterministic modes. They show that under appropriate controllability conditions, this controller guarantees convergence of the probability density to the desired function.
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