This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discret...This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.展开更多
We consider the optimal control problem for a linear conditional McKeanVlasov equation with quadratic cost functional.The coefficients of the system and the weighting matrices in the cost functional are allowed to be ...We consider the optimal control problem for a linear conditional McKeanVlasov equation with quadratic cost functional.The coefficients of the system and the weighting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration.Semi closed-loop strategies are introduced,and following the dynamic programming approach in(Pham and Wei,Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics,2016),we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations.We present several financial applications with explicit solutions,and revisit,in particular,optimal tracking problems with price impact,and the conditional mean-variance portfolio selection in an incomplete market model.展开更多
Purpose The purpose of this paper is to study a new method to improve the performance of the magnet power supply in the experimental ring of HIRFL-CSR.Methods A hybrid genetic particle swarm optimization algorithm is ...Purpose The purpose of this paper is to study a new method to improve the performance of the magnet power supply in the experimental ring of HIRFL-CSR.Methods A hybrid genetic particle swarm optimization algorithm is introduced,and the algorithm is applied to the optimal design of the LQR controller of pulse width modulated power supply.The fitness function of hybrid genetic particle swarm optimization is a multi-objective function,which combined the current and voltage,so that the dynamic performance of the closed-loop system can be better.The hybrid genetic particle swarm algorithm is applied to determine LQR controlling matrices Q and R.Results The simulation results show that adoption of this method leads to good transient responses,and the computational time is shorter than in the traditional trial and error methods.Conclusions The results presented in this paper show that the proposed method is robust,efficient and feasible,and the dynamic and static performance of the accelerator PWM power supply has been considerably improved.展开更多
An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional.The coefficients and the weighting matrices in the cost functional are all assumed to be ...An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional.The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.Closedloop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.In this paper,the existence of an optimal closed-loop strategy for the system(also called the closedloop solvability of the problem)is characterized by the existence of a regular solution to the coupled two(generalized)Riccati equations,together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.展开更多
In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work- space, over serial and conventional parallel systems...In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work- space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional-integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cabledriven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61821004 and 62250056the Natural Science Foundation of Shandong Province under Grant Nos.ZR2021ZD14 and ZR2021JQ24+1 种基金Science and Technology Project of Qingdao West Coast New Area under Grant Nos.2019-32,2020-20,2020-1-4,High-level Talent Team Project of Qingdao West Coast New Area under Grant No.RCTDJC-2019-05Key Research and Development Program of Shandong Province under Grant No.2020CXGC01208.
文摘This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.
基金work is part of the ANR project CAESARS(ANR-15-CE05-0024)lso supported by FiME(Finance for Energy Market Research Centre)and the“Finance et Developpement Durable-Approches Quantitatives”EDF-CACIB Chair。
文摘We consider the optimal control problem for a linear conditional McKeanVlasov equation with quadratic cost functional.The coefficients of the system and the weighting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration.Semi closed-loop strategies are introduced,and following the dynamic programming approach in(Pham and Wei,Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics,2016),we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations.We present several financial applications with explicit solutions,and revisit,in particular,optimal tracking problems with price impact,and the conditional mean-variance portfolio selection in an incomplete market model.
文摘Purpose The purpose of this paper is to study a new method to improve the performance of the magnet power supply in the experimental ring of HIRFL-CSR.Methods A hybrid genetic particle swarm optimization algorithm is introduced,and the algorithm is applied to the optimal design of the LQR controller of pulse width modulated power supply.The fitness function of hybrid genetic particle swarm optimization is a multi-objective function,which combined the current and voltage,so that the dynamic performance of the closed-loop system can be better.The hybrid genetic particle swarm algorithm is applied to determine LQR controlling matrices Q and R.Results The simulation results show that adoption of this method leads to good transient responses,and the computational time is shorter than in the traditional trial and error methods.Conclusions The results presented in this paper show that the proposed method is robust,efficient and feasible,and the dynamic and static performance of the accelerator PWM power supply has been considerably improved.
基金supported by Hong Kong RGC under grants 519913,15209614 and 15224215Jingrui Sun was partially supported by the National Natural Science Foundation of China(11401556)+1 种基金the Fundamental Research Funds for the Central Universities(WK 2040000012)Jiongmin Yong was partially supported by NSF DMS-1406776.
文摘An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional.The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.Closedloop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.In this paper,the existence of an optimal closed-loop strategy for the system(also called the closedloop solvability of the problem)is characterized by the existence of a regular solution to the coupled two(generalized)Riccati equations,together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.
文摘In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work- space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional-integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cabledriven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.