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Theory and Modern Applications

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)

P̃(k − i,k − j,k): in (3.15)

P̅(k + i,k + j,k): in (3.30)

P̃(k + 1,k − j,k): in (3.16)

P̅(k,k + j,k): in (3.31)

P̃(k + 1,k + 1,k): in (3.17)

PÌ…(k,k,k): in (3.32)