Adaptive Continuous Twisting Algorithm of Third Order

For a triple integrator with Lipschitz disturbances Continuous Twisting Algorithm of Third Order (3-CTA) provides finite-time convergence to zero by means of continuous control signal. However, gains design of 3-CTA needs the knowledge of fourth derivative of the output which is difficult to obtain. In this paper, an adaptive version of 3-CTA is presented. An adaptation law is used in order to increase the gains until a level allowing to reject perturbations and achieving convergence to fourth order sliding set. Additionally, experimental results of the implementation of adaptive 3-CTA on an Inertial Wheel Pendulum are presented.