Combination of terminal sliding mode and finite-time SDRE

The codes simulate finite-time terminal sliding mode and SDDRE for Van der Pol oscillator and a mechanical system.

A novel terminal sliding mode control (TSMC) is introduced to control a class of nonlinear uncertain systems in finite time. TSMC is naturally a finite time controller though the time cannot be set as input, and the convergence time is not exactly known to the user before the execution of the control loop. The sliding surface of the introduced controller is equipped with a finite-time gain that finishes the control task in the desired predefined time. The gain is found by partitioning the state-dependent differential Riccati equation (SDDRE) gain, then arranging the sub-blocks in a symmetric positive-definite structure. The proposed approach was validated and compared with SDDRE and conventional TSMC as independent controllers, applied on a Van der Pole oscillator. The capability of the proposed approach to controlling complex systems was checked by simulating a flapping-wing flying robot (FWFR).

The notations and formulas, control law, etc., may be read in the following paper (the names of the codes are based on the relevant sections of the following article):

Nekoo, S. R., Acosta, J., & Ollero, A. (2022). Combination of terminal sliding mode and finite-time state-dependent Riccati equation: Flapping-wing flying robot control. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 09596518221138627. https://doi.org/10.1177/09596518221138627