Hybrid electric vehicles are powered by an electric system and an internal combustion engine. The components of a hybrid electric vehicle need to be coordinated in an optimal manner for the vehicle to deliver the desired performance. This thesis presents a numerical method based on direct method and orthogonal functions called hybrid functions for optimal power management in hybrid electric vehicles with inequality constraints with or without uncertainty. The approach consists of reducing the optimal control problem to a set of algebraic equations by approximating the state variable which is the energy of electric storage system, and the control variable which is the power of fuel consumption. This approximation uses direct method or orthogonal functions with unknown coefficients. In addition, the inequality constraints are converted to equal constrains. The advantage of the developed method is that its computational complexity is less than that of the dynamic and non-linear programming approaches. Key words Hybrid electric vehicles, Direct method, Hybrid functions, Optimal control, Orthogonal function, Min-max.
