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Table 2 Duality between estimation and control

From: Survey of duality between linear quadratic regulation and linear estimation problems for discrete-time systems

LMMSE estimation LQR
x(k): state variable x(k): state variable
y(k): observed variable u(k): control signal
0: first observation N: last control action
\(K_{j}(k)\): in (3.13) \(\overline{K}_{j}(k)\): in (3.27)
\(R_{\varepsilon (k)}\): in (3.14) \(R_{\mathbf{w}(k)}\): in (3.29)
(k − i,k − j,k): in (3.15) (k + i,k + j,k): in (3.30)
(k + 1,k − j,k): in (3.16) (k,k + j,k): in (3.31)
(k + 1,k + 1,k): in (3.17) (k,k,k): in (3.32)