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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 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

\(K_{p}(k)\): in (2.4)

K(k): in (2.10)

\(R_{\varepsilon (k)}\): in (2.5)

\(R_{\mathbf{w}(k)}\): in (2.11)

P(k + 1): in (2.6)

PÌ…(k): in (2.12)

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