Predefined-Time Convergence Control for High-Order Integrator Systems Using Time Base Generators

In this brief, we propose a control method for high-order integrator systems that achieves predefined-time convergence, i.e., the system is driven to the origin in a desired settling time that can be set as an explicit parameter of the controller and it is achieved independently of the initial conditions. Our method can be applied to any single-input single-output (SISO) controllable linear system, to any SISO nonlinear system that can be transformed to the normal form with stable zero dynamics and to multiple-input multiple-output systems that can be decoupled into SISO subsystems in the previously mentioned forms. The proposed approach is based on the so-called time base generators (TBGs), which are time-dependent functions used to build time-varying control laws. The contribution of this brief is the generalization of the TBGs to develop predefined-time controllers for high-order systems, providing procedures to build the required time-dependent functions. The performance of the proposed controllers is evaluated and compared with finite-time and fixed-time controllers in simulations and experiments. We show the applicability of the proposed approach to control electromechanical systems, in particular for the dynamic control of robotic systems.