Q and R are symmetric matrices that used to construct the cost function in optimal control. In the optimal control problem, we seek a gain to minimize a specified cost function expressed as the integral of a quadratic form in the state x and a second quadratic form in the control u. The advantages of using optimal control are:
1. It's more explicit for the control design for multiple-input and/or
multiple-out system;
2. For seeking an optimum controller, the designer doesn't need to know the
desirable closed-loop pole locations;
3. Optimal control can be used on un-controllable systems.
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