Stable sliding mode control of dynamical systems subject to unknown disturbance

Sliding mode control strategies are best known for ensuring a high degree of system robustness with respect to disturbance with negligible computational overhead. However, such strategies typically require information about lower and upper bounds of disturbance to ensure a stable motion of the system. Such bounds cannot be feasibly obtained in many practical applications. Motivated by this problem, we propose a new approach to sliding mode control of perturbed systems, which involves on-line estimation of unknown disturbance. Indeed, evolution of the disturbance is modeled as a random value with parameters determined from a number of past samples. Then, an appropriate disturbance estimator is defined in order to minimize the future effect of this disturbance on sliding motion of the system. It is demonstrated that the proposed approach guarantees a stable and robust response of the system even when no prior information about disturbance is available.