RMPC‐based security problem for polytopic uncertain system subject to deception attacks and persistent disturbances

Abstract

This study investigates the security problem for a class of polytopic uncertain systems by virtue of robust model predictive control (RMPC) approach. In consideration of the difficulties in accessing the system states, a novel dynamic-output-feedback RMPC strategy is presented to guarantee the security of the discussed system subject to randomly occurring deception attacks and persistent bounded disturbances. Such the randomly occurring attack is characterised by using a Bernoulli binary distributed white sequence with a given successful probability. Under this condition, a novel concept of system security in mean-square sense is presented based on RMPC technique, in which the system is required not only to satisfy the specified performance index but also to keep all the states in an invariant set by designing a time-varying terminal constraint set. Moreover, due to the presence of the persistent bounded disturbances and model uncertainties, the worst-case cost function is considered. By using a Lyapunov function approach dependent of the input-to-state stability (ISS), the dynamic-output-feedback RMPC scheme is designed by solving an optimisation problem including some inequality constraints, and the upper bound of the investigated cost function is obtained. In addition, the ISS performance is ensured for the polytopic uncertain system with both the randomly occurring deception attacks and persistent disturbances. Finally, a numerical simulation example is developed to show the effectiveness of the proposed dynamic-output-feedback RMPC strategy.