Combined powertrain and velocity optimization can achieve significant energy efficiency improvements. However, due to the multi-time scales in the system, the optimization is performed hierarchically and by separating time scales. To enforce state constraints, iteration between controller is introduced, for example using Lagrange multipliers as metric for constraint violation. In this paper, an extension of the Koopman operator theory is presented with to obtain a data-driven approximation of the multipliers' behavior, hence eliminating the need for iterations. Because the evolution of the Lagrange multipliers is the result of a fast dynamics optimization problem, and not the response of a nonlinear dynamical system, a novel technique in which the Lagrange multipliers are interpreted as a dynamic system is presented here. The approximate Koopman linear system is then derived using extended dynamic mode decomposition and it is integrated with the slow dynamic optimization. Results show that the Koopman augmented controller, which is solved as one single optimization, meets state and input constraints and achieves similar energy savings compared to an iterative approach.

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