A Non-conservative Robust Output Feedback MPC for Constrained Linear Systems

Model predictive control is an advanced control strategy with a large number of applications. The ability to handle multi-variable problems easily while satisfying input and state constraints make this approach highly appealing. However, when uncertainties are present, a robust scheme is required to ensure stability and satisfaction of constraints. Robustness however should not lead to a drastic deterioration of the performance in the nominal case. One kind of uncertainties that require a robust behavior are disturbances and uncertain model parameters, another uncertain influence comes from measurement errors and state estimation. While most MPC approaches assume that exact state information is available at every time step in the MPC formulation, this is not realistic. Normally not all the states are measured and the measurements are corrupted by noise. Because of the presence of constraints, the separation principle does not hold even in the case of linear systems and hence an output feedback scheme needs to be devised such that the estimation error is accounted for in addition to plant-model mismatch and disturbances. In this work, we propose and demonstrate a non-conservative output feedback scheme within the multi-stage MPC framework for linear time-invariant systems.