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Linear-Quadratic-Gaussian Control

MIMO control design, Kalman filter design, state estimators


lqr Linear-Quadratic Regulator (LQR) design
lqry Form linear-quadratic (LQ) state-feedback regulator with output weighting
lqi Linear-Quadratic-Integral control
dlqr Linear-quadratic (LQ) state-feedback regulator for discrete-time state-space system
lqrd Design discrete linear-quadratic (LQ) regulator for continuous plant
kalman Kalman filter design, Kalman estimator
kalmd Design discrete Kalman estimator for continuous plant
extendedKalmanFilter Create extended Kalman filter object for online state estimation
unscentedKalmanFilter Create unscented Kalman filter object for online state estimation
correct Correct state and state estimation error covariance using extended or unscented Kalman filter and measurements
predict Predict state and state estimation error covariance at next time step using extended or unscented Kalman filter
clone Copy online state estimation object
lqg Linear-Quadratic-Gaussian (LQG) design
lqgreg Form linear-quadratic-Gaussian (LQG) regulator
lqgtrack Form Linear-Quadratic-Gaussian (LQG) servo controller
augstate Append state vector to output vector
norm Norm of linear model


Kalman Filter Estimate states of discrete-time or continuous-time linear system

Examples and How To

Design Yaw Damper for Jet Transport

This case study illustrates the classical design process.

Design an LQG Regulator

Design an LQG regulator for a plant output in a system with noise.

Design an LQG Servo Controller

Design an LQG servo controller using a Kalman state estimator.

Design an LQR Servo Controller in Simulink

Design an LQR controller for a system modeled in Simulink®.

Kalman Filter Design

This example shows how to perform Kalman filtering.

State Estimation Using Time-Varying Kalman Filter

Estimate states of linear systems using time-varying Kalman filters in Simulink.

Nonlinear State Estimation Using Unscented Kalman Filter

This example shows how to use the unscented Kalman filter algorithm for nonlinear state estimation for the van der Pol oscillator.

Validate Online State Estimation at the Command Line

Validate online state estimation that is performed using extended and unscented Kalman filter algorithms.

Generate Code for Online State Estimation in MATLAB

Deploy extended and unscented Kalman filters using MATLAB® Coder™ software.


Linear-Quadratic-Gaussian (LQG) Design

Linear-quadratic-Gaussian (LQG) control is a state-space technique that allows you to trade off regulation/tracker performance and control effort, and to take into account process disturbances and measurement noise.

LQG Regulation: Rolling Mill Case Study

Use linear-quadratic-Gaussian techniques to regulate the beam thickness in a steel rolling mill.

Kalman Filtering

This case study illustrates Kalman filter design and simulation for both steady-state and time-varying Kalman filters.

Extended and Unscented Kalman Filter Algorithms for Online State Estimation

Description of the underlying algorithms for state estimation of nonlinear systems.


Troubleshoot Online State Estimation

Troubleshoot online state estimation performed using extended and unscented Kalman filter algorithms.

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