Robust model predictive control of constrained linear systems with bounded disturbances
A robust model predictive controller is proposed in which the initial state of the nominal/ref\-er\-ence model involved in the on-line optimization is a free decision variable, in addition to the control signals. It is shown that the value of the associated Lyapunov function is zero in the disturbance invariant set \(Z\). The set \(Z\) serves as the ``origin'' for the uncertain system when bounded disturbances are present. Based on this novelty, the robust attractivity and robust exponential stability of the set \(Z\) is established. Also, it is shown that the effective terminal set for the ``tube'' of trajectories emanating from the initial state in the uncertain case is not restricted. The obtained results depend on linearity and cannot easily be extended to nonlinear systems. The benefits of the proposed controller are exposed on the constrained sampled double integrator example.
scientific article; zbMATH DE number 2137843