The synthesis of optimal controllers for multivariable systems usually requires an accurate linear model of the plant dynamics. Real systems, however, contain nonlinearities and high-order dynamics that may be difficult to model using conventional techniques. This paper presents a novel learning method for the synthesis of LQR controllers that doesn't require explicit modeling of the plant dynamics. This method utilizes the sign of Jacobian and gradient descent techniques to iteratively reduce the LQR objective function. It becomes easier and more convenient because it is relatively very easy to get the sign of Jacobian instead of its Jacobian. Simulations involving an overhead crane and a hydrofoil catamaran show that the proposed LQR-LC algorithm improves controller performance, even when the Jacobian information is estimated from input-output data.
