## 1 Introduction  
The need for resonant converters is prominent in the field of induction heating in the metal industry [1], domestic induction cooking [2], and pulsed-power plasma applications [3]. Magnetic levitation systems for a variety of transportation solutions [4], wireless power supplies/chargers for electric vehicles [5, 6], cellphones [7], and biomedical implants [8] are also based on resonant conversion. A typical resonant power delivery system utilizes an inverter (or DC-AC converter [9, 10]) to create an alternating-current (AC) flow through a coil for the generation of alternating magnetic flux, inducing a voltage across a secondary coil or workpiece [11, 12]. The equivalent load \"seen\" by the inverter may be represented by a series resistor-inductor (RL) arrangement, as shown in Figure 0(a)0(a). In this model, the energy transferred to the load is represented by the equivalent resistance \(R\), while the equivalent inductance \(L\) reflects the magnetic behavior of the system. Typical resonant converters operate at relatively high switching frequencies \(\omega_{s}\) (several tens of rad/s up to several \(\mathrm{Mrad/s}\)). As a result, the equivalent inductance impedance \(j\omega_{s}L\) limits the amount of power transferred to the load by increasing the impedance of the equivalent load \"seen\" by the inverter to \(1\,Z_{\alpha\alpha}(\omega_{s})\,|=(R^{2}+(\omega_{s}L)^{2})^{0.5}\). To overcome this limitation, a common solution is adding a resonant capacitor \(C\) in series with the coil, as shown in Figure 0(b)[14]. As a result, the equivalent load impedance \"seen\" by the inverter becomes \(1\,Z_{\alpha\beta}(\omega_{s})\,|=(R^{2}+(\omega_{s}L-1/\omega_{s}C)^{2})^{0.5}\) so that the inductance contribution is offset by that of the capacitance. If \(\mid\omega_{s}L-1/\omega_{s}C\mid<\omega_{s}L\), then \(\mid Z_{eq,d}(\omega_{s})\mid\)\(<\mid Z_{eq,d}(\omega_{s})\mid\), and the power transferred to the load by the same inverter increases. Another typical challenge in the process of resonant power delivery is the time-varying nature of equivalent resistance and/or inductance due to, e.g., workpiece state-of-matter changes in induction heating applications and load/coupling coefficient variations in wireless power transfer applications. In addition, the value of the resonant capacitor may also drift due to temperature variations, high-current-flow-induced mechanical stresses, and degradation [15]. As a result, the equivalent load impedance \"seen\" by the inverter varies (relatively slowly) during the process. Consequently, a feedback control system is employed to counteract these variations by adjusting the inverter's operational state (output voltage and/or frequency) accordingly. This is successfully accomplished in long processes, such as metal processing and battery charging. However, the above-mentioned challenge is critical in pulsed-power applications [16], such as hydrogen fusion. In fusion systems, magnetic levitation and induction heating are simultaneously carried out during a process in which the hydrogen is rapidly heated to a high temperature by an intensive short-time (millisecond-order) power burst for gas-to-plasma conversion. In case energy delivery maximization is the goal, the impedance \"seen\" by the inverter should be minimized by keeping the system at resonance (forcing \(\omega_{s}L-1/\omega_{s}C=0\), as shown in Figure 1b). Meanwhile, if it is desired to stabilize the power delivered to the load at a certain reference value, then the current (and, hence, \(\mid Z_{eq,b}(\omega_{s})\mid\)) should be regulated. However, the values of RLC network parameters are expected to vary due to the above-mentioned reasons. Therefore, the feedback control system must react very quickly (within the fraction of the power burst duration) to these changes by varying the operational frequency to restore the desired operation point.