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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.