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In recent years, efficient optimization algorithms for Nonlinear ModelPredictive Control (NMPC) have been proposed, that significantly reduce theon-line computational time. In particular, direct multiple shooting andSequential Quadratic Programming (SQP) are used to efficiently solve NonlinearProgramming (NLP) problems arising from continuous-time NMPC applications. Oneof the computationally demanding steps for on-line optimization is thecomputation of sensitivities of the nonlinear dynamics at every samplinginstant, especially for systems of large dimensions, strong stiffness, and whenusing long prediction horizons. In this paper, within the algorithmic frameworkof the Real-Time Iteration (RTI) scheme based on multiple shooting, an inexactsensitivity updating scheme is proposed, that performs a partial update of theJacobian of the constraints in the NLP. Such update is triggered by using aCurvature-like Measure of Nonlinearity (CMoN), so that only sensitivitiesexhibiting highly nonlinear behaviour are updated, thus adapting to systemoperating conditions and possibly reducing the computational burden. Anadvanced tuning strategy for the updating scheme is provided to automaticallydetermine the number of sensitivities being updated, with a guaranteed boundederror on the Quadratic Programming (QP) solution. Numerical and controlperformance of the scheme is evaluated by means of two simulation examplesperformed on a dedicated implementation. Local convergence analysis is alsopresented and a tunable convergence rate is proven, when applied to the SQPmethod.

An Adaptive Partial Sensitivity Updating Scheme for Fast Nonlinear Model Predictive Control