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One of the building blocks of the Stellantis hybrid powertrain embedded control software computes the maximum and minimum values of objective functions, such as output torque, as a function of engine torque, hybrid motor torque and other variables. To test such embedded software, an offline reference function was created. The reference function calculates the ideal minimum and maximum values to be compared with the output of the embedded software. This article presents the offline reference function with an emphasis on mathematical novelties. The reference function computes the minimum and maximum points of a linear objective function as a function of six independent variables, subject to 42 linear and two nonlinear constraints. Concave domains, curved surfaces, disjoint domains and multiple local extremum points challenge the algorithm. As a theorem, the conditions and methods for running trigonometric calculations in 6D Euclidean space are presented.

Stringent requirements for high fuel economy and energy efficiency mandate using increasingly complex vehicle thermal systems in most types of electrified vehicles (xEVs). Enabling the maximum benefits of such complex thermal systems under the full envelope of their operating modes demands designing complex thermal control systems. This is becoming one of the most challenging problems for electrified vehicles. Typically, the thermal systems of such vehicles have several modes of operation, constituting nonlinear multiple-input/multiple-output (MIMO) dynamic systems that cannot be efficiently controlled using classical or rule based strategies. This paper covers the different steps towards the design of a model-based control (MBC) strategy that can improve the overall performance of xEV thermal control systems. To achieve the above objective, the latter MBC strategy is applied to control cooling of the cabin and high voltage battery.