Adaptive system to control a pedal-assisted bicycle comprising an electric motor configured to operate as a motor and as a generator associated with a wheel of the bicycle, a rechargeable battery having a power exchange relationship with the electric motor, a pedal-thrust group to be pedaled by a cyclist, a transmission operatively interposed between the pedal-thrust group and a wheel of the bicycle comprising a free-wheel mechanism, the system comprising: - a sensor configured to generate a signal representative of an angular speed (ω wheel) of a wheel of the bicycle; - a sensor configured to generate a signal representative of an angular speed (ω free-wheel) of the free-wheel mechanism; - a sensor configured to generate a signal representative of a state of charge (SoC) of the battery; - a nominal control module configured to generate a motor nominal command signal (I° motor) based at least on said signals representative of the angular speed (ω wheel) of the wheel and of the angular speed (ω free-wheel) of the free-wheel mechanism, wherein said motor nominal command signal (I° motor) or a portion (i° cyclist) thereof is defined by an inversion speed (v limit) of the bicycle beneath which the motor supplies an assistance to the pedal-thrust and above which the motor operates as a generator when the moving bicycle is in a traction condition in which the speed of the wheel of the bicycle is substantially equal to the speed of the free-wheel mechanism, and wherein said motor nominal command signal (I° motor) or a portion (i° cyclist) thereof is further defined by a maximum energy recovery value (i rec,min) when the pedal-thrust group has no traction and when the bicycle is not braking; - an adaptive control module configured to: • generate a motor corrected command signal (I° motor,corr) determined from the motor nominal command signal (I° motor) corrected based on the signal representative of the state of charge (SoC) of the battery; wherein the adaptive control system is further configured to supply to the motor a reference command signal (I° ref) determined based on said motor corrected command signal (I° motor,corr) characterized in that the adaptive control module (1320,1323,1325) is further configured to modify said inversion speed and said maximum energy recovery value (Tc) of the motor nominal command signal or of a portion thereof based on the signal representative of the state of charge (SoC). - a sensor configured to generate a signal representative of an angular speed (ω wheel) of a wheel of the bicycle; - a sensor configured to generate a signal representative of an angular speed (ω free-wheel) of the free-wheel mechanism; - a sensor configured to generate a signal representative of a state of charge (SoC) of the battery; - a nominal control module configured to generate a motor nominal command signal (I° motor) based at least on said signals representative of the angular speed (ω wheel) of the wheel and of the angular speed (ω free-wheel) of the free-wheel mechanism, wherein said motor nominal command signal (I° motor) or a portion (i° cyclist) thereof is defined by an inversion speed (v limit) of the bicycle beneath which the motor supplies an assistance to the pedal-thrust and above which the motor operates as a generator when the moving bicycle is in a traction condition in which the speed of the wheel of the bicycle is substantially equal to the speed of the free-wheel mechanism, and wherein said motor nominal command signal (I° motor) or a portion (i° cyclist) thereof is further defined by a maximum energy recovery value (i rec,min) when the pedal-thrust group has no traction and when the bicycle is not braking; - an adaptive control module configured to: • generate a motor corrected command signal (I° motor,corr) determined from the motor nominal command signal (I° motor) corrected based on the signal representative of the state of charge (SoC) of the battery; wherein the adaptive control system is further configured to supply to the motor a reference command signal (I° ref) determined based on said motor corrected command signal (I° motor,corr) characterized in that the adaptive control module (1320,1323,1325) is further configured to modify said inversion speed and said maximum energy recovery value (Tc) of the motor nominal command signal or of a portion thereof based on the signal representative of the state of charge (SoC). • generate a motor corrected command signal (I° motor,corr) determined from the motor nominal command signal (I° motor) corrected based on the signal representative of the state of charge (SoC) of the battery;