Generally, it is not easy to get a suitable controller for multi variable systems. If the modeling equation of the system can be found, it is possible to get LQR controller as an optimal solution. This paper suggests an LQR learning method tc design LQR controller without the modeling equation. The proposed algorithm uses the same cost function with errol and input energy as LQR is used, and the LQR controller is trained to reduce the function. In this training process, the; Jacobian matrix that informs the converging direction of the controller is used. Jacobian means the relationship of output variations for input variations and can be approximately found by the simple experiments. In the simulations of 2 hydrofoil catamaran with multi variables, it can be confirmed that the training of LQR controller is possible by using the; approximate Jacobian matrix instead of the modeling equation and this controller is not worse than the traditional LQR controller.
