We investigate the dynamics of a two-level quantum system driven by a laser pulse characterized by Lorentzian frequency and sub-Lorentzian amplitude modulations.Complete analytical solutions,expressed via confluent He...We investigate the dynamics of a two-level quantum system driven by a laser pulse characterized by Lorentzian frequency and sub-Lorentzian amplitude modulations.Complete analytical solutions,expressed via confluent Heun functions,are derived.Our analysis reveals that explicit exact analytical solutions exist under infinite sets of specific parameter conditions.The effects of modulation parameters and initial conditions on the final transition probabilities are examined analytically and numerically.Furthermore,the method is demonstrated to be directly applicable to two closely related models with Lorentzian pulses.展开更多
For uncertain strict-feedback systems under the prescribed performance control(PPC)problem,an innovative adaptive prescribed-time tracking control method is proposed.This method combines a novel error transformation f...For uncertain strict-feedback systems under the prescribed performance control(PPC)problem,an innovative adaptive prescribed-time tracking control method is proposed.This method combines a novel error transformation function with the prescribed-time stability theory,thereby achieving exact tracking of desired trajectories within a prescribed time while ensuring that the tracking error stays within predefined boundaries globally.By integrating a newly-designed Lyapunov-like energy function with dynamic surface control,it resolves the error surface issues that result in the semi-global boundedness of tracking error in traditional approaches.Furthermore,through a generalized Filippov solution definition,this approach overcomes the issue of non-existence of the system solution,which arises during the prescribed-time stability analysis due to the discontinuous control input.Simulation results validate the effectiveness of the proposed method.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11965011。
摘要We investigate the dynamics of a two-level quantum system driven by a laser pulse characterized by Lorentzian frequency and sub-Lorentzian amplitude modulations.Complete analytical solutions,expressed via confluent Heun functions,are derived.Our analysis reveals that explicit exact analytical solutions exist under infinite sets of specific parameter conditions.The effects of modulation parameters and initial conditions on the final transition probabilities are examined analytically and numerically.Furthermore,the method is demonstrated to be directly applicable to two closely related models with Lorentzian pulses.
基金supported by the National Natural Science Foundation of China(62503335,92267101,62573301)。
摘要For uncertain strict-feedback systems under the prescribed performance control(PPC)problem,an innovative adaptive prescribed-time tracking control method is proposed.This method combines a novel error transformation function with the prescribed-time stability theory,thereby achieving exact tracking of desired trajectories within a prescribed time while ensuring that the tracking error stays within predefined boundaries globally.By integrating a newly-designed Lyapunov-like energy function with dynamic surface control,it resolves the error surface issues that result in the semi-global boundedness of tracking error in traditional approaches.Furthermore,through a generalized Filippov solution definition,this approach overcomes the issue of non-existence of the system solution,which arises during the prescribed-time stability analysis due to the discontinuous control input.Simulation results validate the effectiveness of the proposed method.