In this note an approximate Bayesian One-Step-Ahead Regulator is described. The design of the regulator is based on first and second moments of the probability distribution of the system parameters. This approach is contrasted with the usual approach of using only the first moments in the standard minimum variance controller. In the case where the output of the system is linear in the parameters, the second moment Bayesian control law has superior expected one step ahead performance. The Bayesian control law is easily implemented in the form of a finite dimensional feedback control law.
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