Abstract <p>This paper presents an analysis of the dynamic properties of a vibration protection system with a dynamic damper interacting with a moving base via a controlled friction damper. By applying dynamic programming theory to vibration protection systems as cyclically controlled objects, relationships are derived that, by linking the components of the system’s state vector and the control, enable the implementation of a local minimum principle procedure for finding the optimal positional control function for typical performance indicators that are clearly independent of control. For the vibration protection system under study with a controlled dynamic damper, optimal positional control of the intermittent damping process is found. It is established that this system possesses unique antiresonance and shock-resistant properties: resonant phenomena are eliminated, and transient processes are damped within a single period.</p>