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 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
LQGRegulator also accepts nonlinear systems specified by AffineStateSpaceModel and NonlinearStateSpaceModel.
For nonlinear systems, the operating values of state and input variables are taken into consideration when constructing the LQGRegulator.
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: