Output feedback Robust tube based MPC for tracking of piece-wise constant references

This paper presents a novel formulation of a robust output feedback model predictive controller to track piecewise constant references (output feedback RMPCT). The real plant is assumed to be modelled as a linear system with additive bounded uncertainties on the states. Under mild assumptions, the proposed MPC can steer the uncertain system in an admissible evolution to any admissible steady state, that is, under any change of the set point. The proposed output feedback controller consists of a stable state estimator and a recently developed robustly stabilizing, tube based, model predictive control for tracking. Feasibility of the proposed controller for any admissible setpoint is achieved by adding an artificial steady state as decision variable. Robust constraint satisfaction is guaranteed by tube-based approach and considering nominal predictions. Robust stability and convergence to (a neighborhood of) the desired steady state is ensured by considering a modified cost function and an extended terminal constraint. The cost function penalizes the tracking error with the artificial reference and the deviation between the artificial and desired steady state; the terminal constraint restricts the terminal state and the artificial steady state. The optimization problem to be solved is a quadratic programming problem, which allows explicit implementations. Robust stability is guaranteed under mild conditions which allows one to consider tracking specifications and disturbance rejection conditions. Moreover, a simple method to achieve offset-free control, compensating the steady tracking error of the outputs, is presented.