In this paper,we consider a class of optimal control problems where the dynamical systems are time-delay switched systems with the delay being a function of time.By applying the control parameterization method,the con...In this paper,we consider a class of optimal control problems where the dynamical systems are time-delay switched systems with the delay being a function of time.By applying the control parameterization method,the control heights and switching times become decision variables that need to be optimized.It is well-known that,for this type problem,the variable switching times cannot be optimized directly.To work around this problem,we introduce a time-scaling transformation technique so that the original system is transformed an equivalent system,which is defined on a new time horizon with fixed switching times.Based on the relationship between the original time scale and the new time scale,we derive the gradients of the objective and constraint functions with respect to the control heights and durations.Then,the new problem can be solved by gradient-based optimization approach.To demonstrate the effectiveness of the time-scaling transformation technique,two example problems are solved.展开更多
Particle accelerators are devices used for research in scientific problems such as high energy and nuclear physics.In a particle accelerator, the shape of particle beam envelope is changed dynamically along the forwar...Particle accelerators are devices used for research in scientific problems such as high energy and nuclear physics.In a particle accelerator, the shape of particle beam envelope is changed dynamically along the forward direction. Thus, this reference direction can be considered as an auxiliary "time" beam axis. In this paper, the optimal beam matching control problem for a low energy transport system in a charged particle accelerator is considered. The beam matching procedure is formulated as a finite "time" dynamic optimization problem, in which the Kapchinsky-Vladimirsky(K-V) coupled envelope equations model beam dynamics. The aim is to drive any arbitrary initial beam state to a prescribed target state, as well as to track reference trajectory as closely as possible, through the control of the lens focusing strengths in the beam matching channel. We first apply the control parameterization method to optimize lens focusing strengths, and then combine this with the time-scaling transformation technique to further optimize the drift and lens length in the beam matching channel. The exact gradients of the cost function with respect to the decision parameters are computed explicitly through the state sensitivity-based analysis method. Finally, numerical simulations are illustrated to verify the effectiveness of the proposed approach.展开更多
The time-scaling transformation is a widely used approach within the computational framework of control parameterization for optimizing the switching times of control variables.However,the conventional time-scaling tr...The time-scaling transformation is a widely used approach within the computational framework of control parameterization for optimizing the switching times of control variables.However,the conventional time-scaling transformation has the limitation that the switching times and the number of switches for each control component must be the same.In this paper,we present a novel technique to solve constrained optimal control problems that allows for adaptively optimizing the switching times for each control component.Numerical results demonstrate that this proposed method provides better flexibility in control strategy and yields improved performance.展开更多
基金This work was supported by the National Natural Science Foundation of China(Nos.11871039 and 11771275).
文摘In this paper,we consider a class of optimal control problems where the dynamical systems are time-delay switched systems with the delay being a function of time.By applying the control parameterization method,the control heights and switching times become decision variables that need to be optimized.It is well-known that,for this type problem,the variable switching times cannot be optimized directly.To work around this problem,we introduce a time-scaling transformation technique so that the original system is transformed an equivalent system,which is defined on a new time horizon with fixed switching times.Based on the relationship between the original time scale and the new time scale,we derive the gradients of the objective and constraint functions with respect to the control heights and durations.Then,the new problem can be solved by gradient-based optimization approach.To demonstrate the effectiveness of the time-scaling transformation technique,two example problems are solved.
基金supported by the National Natural Science Foundation of China(61703114,61673126,61703217,U1701261)the Science and Technology Plan Project of Guangdong(2014B090907010,2015B010131014)
文摘Particle accelerators are devices used for research in scientific problems such as high energy and nuclear physics.In a particle accelerator, the shape of particle beam envelope is changed dynamically along the forward direction. Thus, this reference direction can be considered as an auxiliary "time" beam axis. In this paper, the optimal beam matching control problem for a low energy transport system in a charged particle accelerator is considered. The beam matching procedure is formulated as a finite "time" dynamic optimization problem, in which the Kapchinsky-Vladimirsky(K-V) coupled envelope equations model beam dynamics. The aim is to drive any arbitrary initial beam state to a prescribed target state, as well as to track reference trajectory as closely as possible, through the control of the lens focusing strengths in the beam matching channel. We first apply the control parameterization method to optimize lens focusing strengths, and then combine this with the time-scaling transformation technique to further optimize the drift and lens length in the beam matching channel. The exact gradients of the cost function with respect to the decision parameters are computed explicitly through the state sensitivity-based analysis method. Finally, numerical simulations are illustrated to verify the effectiveness of the proposed approach.
基金Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice(No.22DZ2229014)Science and Technology Commission of Shanghai Municipality(No.20JC1413900).
文摘The time-scaling transformation is a widely used approach within the computational framework of control parameterization for optimizing the switching times of control variables.However,the conventional time-scaling transformation has the limitation that the switching times and the number of switches for each control component must be the same.In this paper,we present a novel technique to solve constrained optimal control problems that allows for adaptively optimizing the switching times for each control component.Numerical results demonstrate that this proposed method provides better flexibility in control strategy and yields improved performance.
