System comprising: - a hydraulic pressure amplifying device comprising: - a casing (10; 100) including at least one low-pressure inlet chamber (12; 112, 113) and at least one high-pressure outlet chamber (14; 114.1, 114.2) with different cross sections which house a staged piston (20; 120) comprising two piston sections (22, 24; 122, 124.1, 124.2) with cross sections respectively matching the chambers (12, 14; 112, 113, 114.1, 114.2), - a feed inlet - means (30; 130) for controlling the movement of the piston (20; 120), the control means being formed - by a distributor (30; 130) which controls the feeding of the or of each low-pressure inlet chamber (12; 112, 113) and - by an electronic control of the distributor, the control means also comprising: - a flow restriction between the feed inlet and the distributor (30; 130), and/or - a flow restriction between the feed inlet and the or each outlet chamber (14; 114.1, 114.2) characterized in that the system comprises means for estimating the ends-of-stroke of the piston (20; 120), the estimation means being configured to estimate the ends-of-stroke of the piston without an end-of-stroke sensor or a mechanical end-of-stroke stop and to control the electronic control. - a hydraulic pressure amplifying device comprising: - a casing (10; 100) including at least one low-pressure inlet chamber (12; 112, 113) and at least one high-pressure outlet chamber (14; 114.1, 114.2) with different cross sections which house a staged piston (20; 120) comprising two piston sections (22, 24; 122, 124.1, 124.2) with cross sections respectively matching the chambers (12, 14; 112, 113, 114.1, 114.2), - a feed inlet - means (30; 130) for controlling the movement of the piston (20; 120), the control means being formed - by a distributor (30; 130) which controls the feeding of the or of each low-pressure inlet chamber (12; 112, 113) and - by an electronic control of the distributor, the control means also comprising: - a flow restriction between the feed inlet and the distributor (30; 130), and/or - a flow restriction between the feed inlet and the or each outlet chamber (14; 114.1, 114.2) characterized in that the system comprises means for estimating the ends-of-stroke of the piston (20; 120), the estimation means being configured to estimate the ends-of-stroke of the piston without an end-of-stroke sensor or a mechanical end-of-stroke stop and to control the electronic control. - a casing (10; 100) including at least one low-pressure inlet chamber (12; 112, 113) and at least one high-pressure outlet chamber (14; 114.1, 114.2) with different cross sections which house a staged piston (20; 120) comprising two piston sections (22, 24; 122, 124.1, 124.2) with cross sections respectively matching the chambers (12, 14; 112, 113, 114.1, 114.2), - a feed inlet - means (30; 130) for controlling the movement of the piston (20; 120), the control means being formed - by a distributor (30; 130) which controls the feeding of the or of each low-pressure inlet chamber (12; 112, 113) and - by an electronic control of the distributor, the control means also comprising: - a flow restriction between the feed inlet and the distributor (30; 130), and/or - a flow restriction between the feed inlet and the or each outlet chamber (14; 114.1, 114.2) characterized in that the system comprises means for estimating the ends-of-stroke of the piston (20; 120), the estimation means being configured to estimate the ends-of-stroke of the piston without an end-of-stroke sensor or a mechanical end-of-stroke stop and to control the electronic control.