This paper considers the discrete model of the cart-pendulum system modeled by discrete mechanics, which is known as a good discretizing method for mechanical systems and has not been really applied to control theory. We first sum up basic concepts on discrete mechanics and discuss the explicitness of the linear approximation of the discrete Euler-Lagrange Equations. Next, the discrete cart-pendulum system is derived and analyzed from the viewpoint of solvability of implicit nonlinear control systems. We then show a control algorithm to stabilize the discrete cart-pendulum based on the discrete-time optimal regulator theory. Finally, some simulations are shown to demonstrate the effectiveness of the proposed algorithm.

This letter is devoted to derivation of a transformation law which converts a class of nonlinear affine control systems with n-states and 2-iputs into simpler systems with chained structure. First, we give a problem formulation that we consider throughout this letter. We next introduce a transformation law and gives its mathematical certification. Then, we apply the transformation method to an example and consider control design based on chained structure for the example in order to confirm the effectiveness of our approach.