The Wolfram Language provides powerful functions to compute state-feedback and estimator gains using pole-placement or optimal techniques. In addition, it has functions that directly assemble regulator and estimator models based on design specifications or precomputed gains.

Pole Placement

StateFeedbackGains — feedback gains computed using pole placement

EstimatorGains — estimator gains computed using pole placement

Optimal Control and Estimation

LQRegulatorGains — feedback gains that minimize a quadratic cost function

LQOutputRegulatorGains — feedback gains that minimize a quadratic output cost function

LQEstimatorGains — estimator gains that minimize a quadratic cost function

DiscreteLQRegulatorGains — emulated discrete-time feedback gains

DiscreteLQEstimatorGains — emulated discrete-time estimator gains

Optimal Control with Constraints

ModelPredictiveController — optimal controller with state and control constraints

DiscreteInputOutputModel — general input-output model

Controllers and Estimators

KalmanEstimator — Kalman estimator with specified covariance matrices

LQGRegulator — linear quadratic Gaussian (LQG) regulator

StateOutputEstimator — estimator model with specified gains

EstimatorRegulator — regulator model with specified estimator and feedback gains