Improved data-driven optimal TILC using time-varying input signals

• We propose a DDOTILC for nonlinear systems with time-varying input signals to achieve a final end specification.
• The output dynamics is given as an inner product of the vectors of time-varying partial derivatives and time-varying inputs.
• The time-varying partial derivatives could capture the complicated behavior of the plant more effectively.
• The learning control law is constructed with a nonlinear function of partial derivatives updated by the I/O data iteratively.
• The improved approach is a data-driven control strategy and requires only the measured I/O data.

A new improved data-driven optimal TILC (DDOTILC) is proposed for a class of nonlinear discrete-time systems by using time-varying control input signals to enhance control performance. An equivalent dynamical linear presentation is developed in the iteration domain for the repeatable nonlinear system, where the time-varying partial derivatives of the system with respect to the time-varying control inputs reflect the dynamical characters of the plant. Both the time-varying input signals and time-varying partial derivatives over the entire finite time interval are updated in batches, respectively. The proposed approach is a data-driven control scheme and only the boundedness of the partial derivatives is needed for control system design and analysis. Both rigorous mathematical analysis and the simulation results are provide to verify the applicability and effectiveness of the proposed approach further.