Electrical contactors are relays for interputing high currents (up to 2000 A). They consist of three main distinct parts: the low voltage circuit, the high voltage circuit and the linear actuator that moves the contact. The purpose of this thesis is to design, optimize and control the moving part of a linear actuator without external sensor. Indeed, it is very important to control the closing speed of the actuator in order to minimize the contacts wear. The speed should not be too fast so as not to damage the silver contacts at the impact and not too slow to avoid multiple arcs, which erode the contacts. The thesis is divided into different themes: the sensorless position detection, the optimization of the actuator, the signal processing of the position and the speed by adapting the Kalman filter, and finally the sensorless speed control of the actuator's moving part. Industrial constraints impose, for reasons of cost, a position detection without sensor. To do this, a high frequency signal (1250 Hz), named scan current, is superimposed to the one that drives the actuator's moving part. Then, the total current is filtered to obtain only the scan current. Its amplitude depends on the position because the inductance of the actuator windind varies greatly with the value of the airgap. It is therefore possible to detect the position using only the provided low voltage circuit. The optimization of the actuator is made by combining genetic algorithms and finite element modeling (FEM). The first objective to be achieved by the optimizer is to minimize the material cost of the actuator. Then, knowing the minimum price of the actuator, the cost becomes a constraint when optimizing for the best position detection. The optimal configuration presented in the thesis promotes the variation of inductance versus the position and thus allows the best position detection following the constraints defined by the specifications. The speed of the moving part is the derivative of the position but as this signal is noisy, the resulting speed is not exploitable as it is. Because the memory of the microcontroller is limited, an adapted Kalman filter method, simple and appropriate, is developed to allow filtering of the position and speed. Finally, the study of the speed control is first simulated using Matlab-Simulink in order to test different control strategies in both open and closed loops. They are then verified on the test bench with the industrial contactor and the optimized one. The results allow the validation of the different levels of the method of design, optimization and sensorless control of a linear actuator.