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Abstract

The intensifying need for more energy-efficient transportation is driving the development of advanced control strategies for sustainable mobility. In this thesis, we contribute to these efforts by developing efficient numerical methods that are key to realizing an Ecological Adaptive Cruise Control (EACC) system for an electric vehicle based on Nonlinear Model Predictive Control (NMPC). As an NMPC application, EACC poses several challenges that must be addressed before these methods can be employed, and we tackle those challenges in this work.

NMPC is a closed-loop control strategy that uses a dynamical system’s model to predict and optimize its behavior. The current system state parametrizes an Optimal Control Problem (OCP), which is solved at fixed sampling times to update the control, thereby reacting to disturbances as they occur. A well-established approach for real-time NMPC is to discretize the OCP via Direct Multiple Shooting (DMS), then solve it using the Real-Time Iterations (RTI) scheme or its extension, the Multi-Level Iterations (MLI) scheme. RTI cuts down on computational cost by carrying out a minimal number of tailored Sequential Quadratic Programming (SQP) iterations, exploiting similarities in consecutive OCPs. MLI extends this efficiency by creating a hierarchy of inexact SQP iterations, reusing previous derivative information – a design that is well-suited for EACC, where control updates must be computed quickly on hardware with limited resources.

To fully leverage these schemes in EACC, we must address the first major challenge: the interpolation of multivariate Lookup Tables (LUTs). LUTs are indispensable in realistic vehicle models and their interpolation must preserve vital data ”shapes” like monotonicity or convexity. At the same time, the interpolation must be sufficiently smooth to enable derivative-based optimization. Addressing this, we propose what appears to be the first smooth multivariate shape-preserving interpolation method. Our method can extend any existing univariate smooth shape-preserving interpolation method to higher dimensions.

In addition to ensuring faithful interpolation of LUTs, we further address the treatment of external inputs, such as road elevation and the behavior of preceding vehicles – another essential aspect of realistic vehicle control. Our proposed approaches explicitly incorporate external inputs within the DMS discretization and the RTI and MLI schemes, granting more flexibility in reacting to real-world variations.

Building upon the external input incorporation, we introduce the Sensitivity and External Input Scenario based (SensEIS) feedback strategy, recognizing the limited computational resources in many automotive settings. SensEIS feedback reduces online computations by exploiting precomputed control responses for common driving scenarios. Online, the controller selects the best-matching scenario and updates the control using only a few matrix-vector multiplications or by solving a single Quadratic Program, thus significantly reducing feedback delay.

Alongside these algorithmic developments, we also extend the theory of inexact NMPC by proving asymptotic stability of inexact NMPC for problems modeled by a class of semilinear parabolic Partial Differential Equations (PDEs). This establishes a theoretical underpinning for extending the RTI and MLI schemes to PDE-governed problems. In electric vehicle control, NMPC of PDE-governed systems can be relevant for example in the context of thermal management.

Finally, to assess the potential of our methods, we conduct numerical experiments with real-world driving data. The results show energy savings of over 3.4% compared to the human driver, indicating a significant potential of our methods for advancing sustainable mobility.