A data-driven optimal time-delayed control approach and its application to aerial manipulators

In this paper, a data-driven optimal time-delayed control (TDC) approach is developed for Euler-Lagrange systems and applied to an aerial manipulator. The proposed approach is able to deal with the nonlinearity and handle unmodelled dynamics, model uncertainties and unknown disturbances in Euler-Lagrange systems. The time-delayed estimation employed in the proposed approach uses the measurement information at the last time instant to approximately estimate all the unknown factors at the current time instant. A constant gain matrix is the main design parameter and influences both the closed-loop stability and the tracking performance. Currently, this constant gain matrix is either calculated by using the system model based on a stability condition or obtained by trial and error, both of which are rather time-consuming in practice. The data-driven TDC approach developed in this paper can find the constant gain matrix directly from the input and output data without any knowledge of the inertia matrix. To achieve optimal control performance, an LQR term is integrated in the data-driven design. The input-to-state stability of the closed-loop system is proven. The proposed approach is characterized by easy implementation and low computational efforts. The application to the aerial manipulator and the experiment results with a hexacopter demonstrate the effectiveness of the proposed approach.