An inexact sensitivity updating scheme for fast nonlinear model predictive control based on a curvature-like measure of nonlinearity

In recent years several fast Nonlinear Model Predictive Control (NMPC) strategies have been proposed, aiming at reducing computational burden and widening the scope of NMPC techniques. A promising approach is the Real-Time Iteration (RTI) scheme, where Nonlinear Programming (NLP) problems are parametrized by multiple shooting and only one Sequential Quadratic Programming (SQP) iteration is performed at every sampling instant. A computationally expensive step of RTI is the calculation of sensitivity information of nonlinear dynamics, especially for problems with large system dimensions or long prediction horizons. In this paper, an inexact sensitivity updating scheme to be used in the RTI framework is proposed, that allows to reduce the number of sensitivities updates over the prediction horizon at each sampling instant. A Curvature-like Measure of Nonlinearity (CMoN) of dynamic systems is used as a metric to quantify the linearization reliability, and to trigger sensitivity update only if needed. Numerical simulation results show that the proposed approach can significantly reduce the on-line computational efforts for sensitivity computations without major impact on the control performance.