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Most common approaches to designing powerful picosecond laser systems based on Nd-doped crystals imply stages of pulse generation, regenerative and output amplification. We develop the dynamical operation control scheme utilizing pulsed repetitive pumping, active and passive mode-locking, negative feedback, adjustable loss level in the oscillator cavity and switching to regenerative amplification regime, provides laser pulse formation in each laser shot. It takes several microseconds on the end of pump pulse. This approach actually allows shortest way to obtain just at the laser output near Fourier transform limited picosecond pulses of shortest time width, of more than one millijoule energy with excellent pulse-to-pulse stability and low optical jitter value. Both oscillator and regenerative amplifier can be based on the same single active crystal. Using Fabry-Perot etalons inside oscillator cavity allows significant varying output pulse width which can take values from 15 (with Nd:YLF) or 25 ps (with Nd:YAG) and up to 300 ps. Evolution of pulse energy, spectrum and time profile during a single generation cycle can be well illustrated using universal numerical calculation model which describes pulse formation governed by the operation control and also taking into account the pulse profile modifying due to amplification. Utilizing diode end-pump geometry allows maximal overlapping of resonator mode and pumped volume, whereby providing optimal pump energy conversion efficiency into the output radiation. As a result, using the picosecond Nd:YAG laser based on the described scheme with one end-amplifier stage provides 25 ps pulses more than 5 mJ at fundamental wavelength with repetition rates within ~400Hz. Conversion efficiency in the second harmonic using LBO nonlinear crystals can be more than 60%. Both laser and amplifier use diode end-pumping by means of fiber coupled laser diode arrays of 70 and 120 W maximum peak powers respectively. Owing to pulse regime and end-pump geometry, thermal loading is not high and the system does not require liquid cooling and can be easily power scalable by means of an additional amplification stage. Further increase of output peak power and, respectively, single pulse energy by means of additional amplification stages implies operating near the saturation regime. At high repetition rates and, respectively, average power values, operation conditions strongly depend on thermal lens induced in the laser crystal. Increase of average pump power at longitudinal geometry principally results in aberrational lens formation. Spherical part of the thermal lens may be compensated using usual spherical optics, whereas aberrational part action is more complex. Along with the irretrievable aberrational losses such a lens exhibits a certain adaptive effect that may maintain, to some extent, operation steadiness. An adequate analysis is required for system developing with laser generation mode of acceptable quality and, at the same time, supporting mode locking regime.