In this paper, we study the time optimal control problem in a DC-DC buck converter in the underdamped oscillatory regime. In particular, we derive analytic expressions for the admissible regions in the state space, satisfying the condition that every point within the region is reachable in optimal time with a single switching action. We then make use of the general result to establish the minimum and maximum variation allowed to the load in two predefined design set-ups that fulfills the time optimal single switching criteria. Finally, we make use of numerical simulations to show the performance of the proposed control under changes in the reference voltage and load resistance.

This study presents a mathematical modeling framework to analyze the impact of integrating sterilizing treatment into tuberculosis (TB) control strategies, particularly in resource-limited settings. Our findings highlight that while sterilizing treatment alone is highly effective in reducing TB incidence and mortality, its widespread implementation requires significant financial investment. The optimal control approach demonstrates that a mixed strategy, combining sterilizing and non-sterilizing treatments, can achieve comparable public health benefits at a lower cost, especially in the medium-term planning. From a long-term perspective, however, our results suggest that exclusively sterilizing treatment ultimately leads to greater reductions in TB incidence, prevalence, and mortality, justifying its higher initial cost. This is primarily due to the ability of sterilizing drugs to eliminate latent TB infections, prevent future active infections and disease-induced deaths, and avoid a considerable number of treatments. Additionally, under scenarios where the cost of sterilizing drugs decreases over time, a swift transition to a solely sterilizing treatment could result in both epidemiological and economic advantages for healthcare systems.

This study presents a mathematical modeling framework to analyze the impact of integrating sterilizing treatment into tuberculosis (TB) control strategies, particularly in resource-limited settings. The numerical analysis of the proposed mathematical framework indicates that while sterilizing treatment alone is highly effective in reducing TB incidence and mortality, its widespread implementation requires significant financial investment. The optimal control approach demonstrates that a mixed strategy, combining sterilizing and non-sterilizing treatments, can achieve comparable public health benefits at a lower cost, especially in medium-term planning. From a long-term perspective, however, our results suggest that exclusively sterilizing treatment ultimately leads to greater reductions in TB incidence, prevalence, and mortality, justifying its higher initial cost. This is primarily due to the ability of sterilizing drugs to eliminate latent TB infections, prevent future active infections and disease-induced deaths, and avoid a considerable number of treatments. Additionally, under scenarios where the cost of sterilizing drugs decreases over time, a swift transition to a solely sterilizing treatment could result in both epidemiological and economic advantages for healthcare systems.