Tube-Based Active Robust MPC for Uncertain Constrained Linear Systems With Time Delays

The problem of robust tube-based model predictive control (MPC) is considered for a class of discrete-time constrained linear systems with time-delayed states and additional disturbances. This paper presents an active robust control scheme that can simultaneously cope with disturbances and time-delay states using active approaches, rather than inherent system robustness. The proposed robust controller design methodology is implemented by constructing a minimal robust control-invariant set of nominal linear systems with time-delayed states neglecting additional disturbances. Based on the time-delay-dependent robust MPC approach for the nominal time-delay system, a novel active robust tube-based MPC algorithm considering time-delayed states is proposed. Furthermore, a delay-dependent sufficient condition for the tube-based controller is derived. Based on the implementation of the delay-dependent robust tube-based controller, the novel active control method is much less conservative than previous approaches. Numerical simulation results demonstrate the effectiveness of the proposed method.