A Variational and Symplectic Framework for Model-Free Control: Preliminary Results

The model-free control approach is an advanced control law that requires little information about the process to control. Since its introduction in 2008, numerous applications have been successfully considered demonstrating its robustness in tracking and disturbance rejection. In this work, a variational approach of the model-free control is proposed in order to enhance its robustness capabilities. An adaptive formulation of the controller is proposed using the calculus of variations within a symplectic framework, aiming to formulate the control law as an optimization problem for the online tuning of its key parameter. The proposed formulation establishes a coupling between the model-free control law and a variational integrator to enhance robustness against process variations and emphasize closed-loop stabilization. Illustrative examples are examined to highlight the effectiveness of the proposed approach.