For finite-horizon rate-limited nonlinear stochastic control, R_n(D) satisfies F_n(D) ≤ R_n(D) ≤ F_n(D) + log(F_n(D) + 3.4) + 2 + 1/n bits, establishing directed information as the governing quantity.
Strong functional representation lemma and applications to coding theorems
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Rate-Cost Tradeoffs in Nonlinear Control
For finite-horizon rate-limited nonlinear stochastic control, R_n(D) satisfies F_n(D) ≤ R_n(D) ≤ F_n(D) + log(F_n(D) + 3.4) + 2 + 1/n bits, establishing directed information as the governing quantity.