This paper studies the stability of remotely controlled and observed single-input controllable linear systems under power-constrained pulse-width modulated denial-of-service (DoS) signals. The effect of a DoS jamming signal is to corrupt the communication channels, thus preventing the data from being received at its destination. In this work, we first assume that the DoS signal is partially known, i.e., a uniform lower bound for the off time intervals and the on-to-off transiting time instants are known. We then propose a first type of resilient control and triggering strategies which is provably capable of beating partially known jamming signals. Building on this, we then present our joint control and identification algorithms, JAMCOID for Periodic Signals and JAMCOID, which are provably able to guarantee the system stability under unknown jamming signals. More precisely, the JAMCOID for Periodic Signals algorithm is able to partly identify a periodic DoS signal with known uniform lower bound for the off time intervals, whereas the JAMCOID algorithm is capable of dealing with power-constrained, but otherwise unknown, DoS signals while ensuring stability. The practicality of the proposed techniques is evaluated on a simulation example under partially known and unknown jamming scenarios.