Steering a linear system at the minimum information rate: quantifying redundancy via covariance assignment theory

We compute fundamental performance limitations in the data rate constrained control of continuous-time linear stochastic control systems using information theoretic tools and principles. Specifically, we find the minimum achievable mean square error for steering a linear system to sequences of uncertain steering objectives under a rate constraint as the solution of a convex optimization problem. We propose the redundancy of a control system as a measure of the relative inefficiency of information transmission through a linear control system vs. an ideal communications channel.