Robust Model Predictive Control for Nonlinear Discrete-Time Systems using Iterative Time-Varying Constraint Tightening

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 concerning computational load, conservatism, generality, or implementation complexity have to be made. This work provides a practical balance by proposing a novel receding-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 optimize system operation and the required constraint tightening. Numerical experiments show the effectiveness of the proposed controller for three nonlinear systems. Comparisons with two existing techniques show scenario-dependent tradeoffs, though the proposed controller consistently generates less conservative error sets.