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Machine Learning Methodologies for Electric-Vehicle Energy Management Strategies
Published in Hussein T. Mouftah, Melike Erol-Kantarci, Sameh Sorour, Connected and Autonomous Vehicles in Smart Cities, 2020
John S. Vardakas, Ioannis Zenginis, Christos Verikoukis
PMP methods are analytical methods that are based on the mathematical formulation of the problem, thus they obtain solutions faster compared to other approaches; however, PMPs are offline methods and require the a priori knowledge of the driving cycles [35]. The main idea behind PMP is the fact that it reduces the constrained global optimization problem into a local Hamiltonian minimization problem. PMP has been applied in the EMS proposed in Ref. [23], where the energy management approach is applied to multiple HEVs, given the flexibility in power demand, instead of strictly following the required power from the vehicle level. Similarly, a PMP-based control strategy for HEVs is proposed in Ref. [78], where the optimal control problem based on PMP is converted to a nonlinear programming model, by using the Legendre pseudospectral method. An extension of the PMP, called Approximate PMP, considers a piecewise linear approximation of the engine fuel-rate, in order to obtain a simple convex approximation of the Hamiltonian that is able to achieve a fuel consumption reduction of 6.96% compared to the conventional PMP [29].
Mathematical optimization in enhancing the sustainability of aircraft trajectory: A review
Published in International Journal of Sustainable Transportation, 2020
Ahmed W.A. Hammad, David Rey, Amani Bu-Qammaz, Hanna Grzybowska, Ali Akbarnezhad
The collocation points obtained in the Legendre pseudospectral method correspond to the zeros of a specific Lagrange polynomial expression, i.e. the roots. In Legendre pseudospectral methods, the collocation points used depend on how the roots of the polynomial are obtained. Depending on how the roots are obtained, the collocation points are referred to as either Legendre-Gauss (Guo and Yan, 2009), as the Legendre-Gauss-Radau points (Wang and Guo, 2012), or as the Legendre-Gauss-Lobatto points (Parter, 1999).