Energy-efficient torque allocation for straight-line driving of electric vehicles based on pseudoconvex polynomials

TL;DR

This paper introduces a polynomial-based optimization method for electric vehicle torque allocation that minimizes energy consumption, ensuring robustness and real-time applicability through sum of squares programming and constrained nonlinear optimization.

Contribution

It presents a novel polynomial approximation approach with sum of squares constraints for efficient, robust torque allocation in electric vehicles, enabling real-time optimization.

Findings

Modest reduction in electric energy consumption.

Real-time optimization capability demonstrated.

Robustness against noisy or sparse data achieved.

Abstract

Electric vehicles with multiple motors provide a flexibility in meeting the driver torque demand, which calls for minimizing the battery energy consumption through torque allocation. In this paper, we present an approach to this problem based on approximating electric motor losses using higher-order polynomials with specific properties. To ensure a well-behaved optimization landscape, monotonicity and positivity constraints are imposed on the polynomial models using sum of squares programming. This methodology provides robustness against noisy or sparse data, while retaining the computational efficiency of a polynomial function approximation. The torque allocation problem based on such polynomials is formulated as a constrained nonlinear optimization problem and solved efficiently using readily available solvers. In the nominal case, the first-order necessary conditions for optimality can also be used to obtain a global solution. The performance of the proposed method is evaluated on several certification driving cycles against a grid search-based benchmark. Results show a modest influence on electric energy consumption, while enabling real-time optimization and integration with other vehicle control systems.