Robust MPC with optimized controller dynamics for linear polytopic systems with bounded additive disturbances

Computationally efficient robust model predictive control algorithm applicable for linear systems with polytopic model uncertainty as well as bounded additive disturbances is explored. A form of control scheme consisting of a static state feedback and a dynamically evolving perturbation is used in such a way that the cost function can be minimized in a receding horizon fashion over a pre-determined feasibility set which is invariant to both system parameter variations as well as additive disturbances. The cost minimization scheme used guarantees the convergence of the state to a small disturbance-invariant set in the neighbourhood of the origin. This control scheme is selected over the more conventional static state feedback based receding horizon control scheme because it allows the optimization of the feasible set offline, thus reducing the online computational burden. Simulation results are presented to verify the performance of the algorithm.