What is Q matrix in LQR?

In LQR, Q matrix defines the weights on the states while R matrix defines the weights on the control input in the cost function.

What is cost function in LQR?

The cost function is often defined as a sum of the deviations of key measurements, like altitude or process temperature, from their desired values. The algorithm thus finds those controller settings that minimize undesired deviations.

Is LQR linear?

While solving the dynamic programming problem for continuous systems is very hard in general, there are a few very important special cases where the solutions are very accessible. The simplest case, called the linear quadratic regulator (LQR), is formulated as stabilizing a time-invariant linear system to the origin.

What is an LQR controller?

Linear-Quadratic Regulator (LQR) Controller The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem.

When LQG controller problem is solved in deterministic setting?

When LQG controller problem is solved in a deterministic setting, known as an H 2 optimal control problem, in which the H 2 norm of a certain transfer function from an exogenous disturbance to a pertinent controlled output of a given plant is minimized by appropriate use of an internally stabilizing controller.

What is a linear quadratic regulator (LQR)?

The linear quadratic regulator (LQR) is a well-known design technique that provides practical feedback gains. (Continued on next page) 19.2 Full-State Feedback 93

What is the LQ problem in physics?

The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the main results in the theory is that the solution is provided by the linear–quadratic regulator ( LQR ).