Fast robust model predictive control of high-dimensional systems

In this paper, a fast tube-based algorithm is proposed for robust model predictive control (RMPC) using an uncertain finite step response (FSR) input-output model with time-invariant bounded uncertainty. The use of an FSR model, in place of the high-dimensional state-space model, allows the assurance of good performance while dramatically reducing the online cost of the controller. Bounds on the uncertain FSR coefficients are computed offline from the high-dimensional model or by performing step tests in the plant. Using these bounds, a tube-based RMPC algorithm is employed to guarantee the practical stability of the closed-loop system. The practicality of the algorithm is demonstrated by application to an infinite-dimensional example inspired by the field of tissue engineering.