Robust Model Predictive Control for nonlinear discrete-time systems using iterative time-varying constraint tightening

Abstract: Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load, conservatism, generality, or implementation complexity have to be made, and finding an approach that provides the right balance is still a challenge to the research community. This work provides a contribution by proposing a novel shrinking-horizon robust MPC formulation for nonlinear discrete-time systems. By explicitly accounting for how disturbances and linearization errors are propagated through the nonlinear dynamics, a constraint tightening-based formulation is obtained, with guarantees of robust constraint satisfaction. The proposed controller relies on iteratively solving a Nonlinear Program (NLP) to simultaneously optimize system operation and the required constraint tightening. Numerical experiments show the effectiveness of the proposed controller with three different choices of NLP solvers as well as significantly improved computational speed, better scalability, and generally reduced conservatism when compared to an existing technique from the literature.