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Linear Quadratic Gaussian (LQG) Control

In control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems. It concerns linear systems driven by additive white Gaussian noise. The problem is to determine an output feedback law that is optimal in the sense of minimizing the expected value of a quadratic cost criterion. Output measurements are assumed to be corrupted by Gaussian noise and the initial state, likewise, is assumed to be a Gaussian random vector.

Under these assumptions an optimal control scheme within the class of linear control laws can be derived by a completion-of-squares argument.[1] This control law which is known as the LQG controller, is unique and it is simply a combination of a Kalman filter (a linear–quadratic state estimator (LQE)) together with a linear–quadratic regulator (LQR). The separation principle states that the state estimator and the state feedback can be designed independently. LQG control applies to both linear time-invariant systems as well as linear time-varying systems, and constitutes a linear dynamic feedback control law that is easily computed and implemented: the LQG controller itself is a dynamic system like the system it controls. Both systems have the same state dimension.

from Linear–Quadratic–Gaussian Control - Wikipedia

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State Space, Part 4: What is LQR control?

Mathworks - Brian Douglas
17 min
Beginner
Video
Theory

The Linear Quadratic Regulator (LQR)LQR is a type of optimal control that is based on state space representation. In this video, we introduce this topic at a very high level so that you walk...

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Control Bootcamp: LQG Example in Matlab

Steve Brunton
13 min
Beginner
Video
Theory

This video combines the LQR and Kalman filter in Matlab on the example of an inverted pendulum on a cart. We stabilize the full nonlinear system with a measurement of a single variable (the...

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The Linear Quadratic Regulator (LQR)

Laurent Lessard
Intermediate
Article / Blog
Theory

Lecture notes for ECE717 on LQR control by Laurent Lessard. There is a section that shows how the Algebraic Riccati Equation is part of the LQR solution by "completing the square".

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The Linear Quadratic Regulator

Laurent Lessard
Beginner
Article / Blog
Theory

In these notes, we will derive the solution to the finite-horizon linear quadratic regulator (LQR) problem in several different ways. Fundamentally, LQR can be viewed as a large least...

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