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BUILT-IN MATHEMATICA SYMBOL
LQGRegulator[{ssm, sensors, finputs}, {w, v, h}, {q, r, p}]
constructs the optimal feedback regulator for the StateSpaceModel ssm using noisy measurements sensors and feedback inputs finputs. The process, measurement, and cross-covariance matrices are w, v, and h; and the state, input, and state-input weighting matrices are q, r, and p.
LQGRegulator[{ssm, sensors, finputs, einputs}, {...}, {...}]
specifies einputs as the exogenous deterministic inputs.
Details and Options
- The standard state-space model ssm can be given as StateSpaceModel[{a, b, c, d}], where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
-
continuous-time system 
discrete-time system - The descriptor state-space model ssm can be given as StateSpaceModel[{a, b, c, d, e}] in either continuous time or discrete time:
-
continuous-time system 
discrete-time system - The input
can include stochastic inputs 
, feedback inputs 
, and exogenous deterministic inputs 
. - The arguments finputs and einputs are lists of integers specifying the positions of
and 
in 
. - The output
consists of the noisy measurements 
as well as other outputs. - The argument sensors is a list of integers specifying the positions of
in 
. - LQGRegulator[{ssm, sensors, finputs}, {...}, {...}] is equivalent to LQGRegulator[{ssm, sensors, finputs, None}, {...}].
- If not specified, h and p are assumed to be zero matrices.
- Block diagram of the continuous-time system with its regulator:
- Block diagram of the discrete-time system with its regulator:
- The system with the regulator has the following block diagram:
Examplesopen all
Basic Examples (1)
Construct an LQG regulator for a system with one measured output and one feedback input:
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New in 8 | Last modified in 9
