Robust MPC for Linear Systems with Parametric and Additive Uncertainty: A Novel Constraint Tightening Approach

We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The system dynamics matrices are not known exactly, leading to parametric model mismatch. We also consider the presence of an additive disturbance. Set based bounds for each component of the model uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC controller in closed-loop with the uncertain system, and Input to State Stability of the origin. We highlight the efficacy of our proposed approach via a numerical example.Comment: Draft submitted to Automatica. Second and third authors contributed equall

Regions of attraction and recursive feasibility in robust MPC

For linear systems with multiplicative uncertainty, a formulation of robust model predictive control in a lifted space is given and is proven to give better or equal performance to any tube MPC approach that uses the same parametrisation of the input. Then a tube MPC controller is formulated that ensures recursive feasibility through the use of terminal sets in the degrees of freedom available to the controller. This is shown to give performance comparable to the lifted approach while avoiding an exponential growth in computation