Reset control on a sliding set: Well-posedness, stability and robustness

A reset controller is a continuous-time controller equipped with reset actions, which are instantaneous jumps of the controller state, applied when specific conditions are met. Reset control has been demonstrated to be an effective means of overcoming linear controller limitations in both the time and frequency domains, and it can generate a finite-time response in a unique manner compared to other finite-time controllers. This research proposes a novel reset controller utilizing a resetting law based on a high-order sliding set and a hybrid dynamical system formalism that efficiently addresses the reaching phase. The controller parameters are designed to be feasible, ensuring that the nominal closed-loop hybrid system is well-posed and globally asymptotically stable. Furthermore, well-posedness implies robustness against perturbations such as measurement noise, parametric uncertainty, and actuator disturbances. A case study is examined, providing guidelines for the design of the reset controller and a comprehensive analysis of its robustness characteristics in relation to a high-order sliding mode controller.