NMPC based on Huber penalty functions to handle large deviations of quadrature states

Nonlinear Model Predictive Control for mechanical applications is often used to perform the tracking of time-varying reference trajectories, and is typically implemented using penalty functions based on L₂ norms. Controllers for mechanical systems, however, are often required to handle large deviations from the reference trajectory. In such cases, it has been observed that NMPC schemes based on L₂ norms can have undesirably aggressive behaviors. Heuristics can be developed to tackle these issues, but they require intricate and non-systematic tuning procedures. This paper proposes an NMPC scheme based on Huber penalty functions to handle large deviation of quadrature state from its reference, offering an intuitive and easy-to-tune alternative. The behavior of the proposed NMPC scheme is analysed, and the conditions for its nominal stability are established. The control scheme is illustrated on a simulated crane.