Optimal Nonlinear Regulation of Euler-Lagrange Dynamic Systems

A wide variety of methods are used to solve control problems and find optimal control laws that improve the behavior of systems. In this article, a control law is designed for fully actuated dynamic Lagrange systems, that is, systems that have the characteristic that their control input dimension is the same as the dimension of the generalized position vector, beside their parameters are known and their states are known or can be estimated. Canceling part of the dynamics of the system and using the Pontryagin Theorem, a control law is determined that allows the proposed quadratic criterion to be minimized and that ensures the asymptotic stability of the feedback system in the Lyapunov sense. This control law is implemented for optimal regulation, in one of the known problems of optimization of the carriage with the pendulum.