Robust Model Predictive Control for Linear Systems with State and Input Dependent Uncertainties

This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being non-convex, we are able to handle it as a second-order cone program. Both open-loop and semi-feedback planning strategies are presented. The formulation has linear complexity in the planning horizon length. The approach is thus amenable to efficient real-time implementation with a guarantee on recursive feasibility and global optimality. Robust position control of a satellite is considered as an illustrative example.