BUILT-IN MATHEMATICA SYMBOL

# LQGRegulator

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 OptionsDetails 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:

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Construct an LQG regulator for a system with one measured output and one feedback input:

 Out[1]=

## See AlsoSee Also

New in 8 | Last modified in 9
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