This paper proposes a study of the optimal control problem with state constraint, using two types of a power-assist wheelchair propulsion. The cost function is given by the metabolic function, which represented by acompromise between the work exerted by the joints muscles (mechanical effect) and an efficiency functionthat converts chemical into mechanical energy (biomechanical effect). The dynamic wheelchair is given by asimple model, which connects the push force to the wheelchair speed. An upper bound constraint is consideredin order to limit the energy consumed by the motor. This study used an approach that calls the Pontryagin’smaximum principle, the optimal solution varies with the parameters of the problem. Finally, a numericalcomparison is enabled using two types of assistance: constant and proportional. This numerical comparisonis based on the framework of the optimal control theory with two different costs. The first cost is given by theintegral of the squared user’s force and the second by the integral of the metabolic function. This Numericalresults show that the user provides less effort with metabolic cost than with the energy user’s force.