Hybrid electric vehicle powertrains consist of two or more different energy sources in order to reduce fuel consumption and CO2 emissions. Due to their complexity, these powertrains require adequate control systems, whose design is based on extensive computer-aided optimizations and simulations requiring accurate and computationally-efficient mathematical models. The thesis proposes modeling of hybrid powertrain kinematics and dynamics, as well as their power-flow analysis, based on the grapho-analytical bond graph method. Furthermore, dynamic programming-based powertrain control variable optimization is considered, where the optimization results are used for the control strategy design and verification. Finally, the multi-objective optimization of an extended range electric vehicle component sizing is proposed, by using parameter-optimized scalable control strategy which is based on rule-based control in conjunction with a near-optimal Equivalent consumption minimization strategy.