This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function...This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.展开更多
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
Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method...Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneousiy provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking (LQT) control method.展开更多
In this paper, tile authors first study two kinds of stochastic differential equations (SDEs) with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimen...In this paper, tile authors first study two kinds of stochastic differential equations (SDEs) with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations (BSDEs) driven by Levy pro- cesses, the authors proceed to study a stochastic linear quadratic (LQ) optimal control problem with a Levy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results.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
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
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
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
This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different wa...This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different ways.As a consequence,the open problems raised by Chen and Yong(2007) are solved.To characterize the saddle points more clearly,coupled forward-backward stochastic Volterra integral equations and stochastic Fredholm-Volterra integral equations are introduced.Compared with deterministic game problems,some new terms arising from the procedure of deriving the later equations reflect well the essential nature of stochastic systems.Moreover,our representations and arguments are even new in the classical SDEs case.展开更多
Abstract This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefficients, which is actually a control combining the H2 optimization with the H∞ robust performance as the name of ...Abstract This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefficients, which is actually a control combining the H2 optimization with the H∞ robust performance as the name of H2/H∞ reveals. Based on the classical theory of linear-quadratic (LQ, for short) optimal control, the sufficient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation (BSRE, for short) associated with H∞ robustness are derived. Then the sufficient and necessary conditions for the existence of the H2/H∞ control are given utilizing a pair of coupled stochastic Pdccati equations.展开更多
In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an a...In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates(increases and decreases) between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related:after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.展开更多
Energy management strategies based on optimal control theory can achieve minimum fuel consumption for hybrid electric vehicles, but the requirement for driving cycles known in prior leads to a real-time problem. A rea...Energy management strategies based on optimal control theory can achieve minimum fuel consumption for hybrid electric vehicles, but the requirement for driving cycles known in prior leads to a real-time problem. A real-time optimization power-split strategy is proposed based on linear quadratic optimal control. The battery state of charge sustainability and fuel economy are ensured by designing a quadratic performance index combined with two rules. The engine power and motor power of this strategy are calculated in real-time based on current system state and command, and not related to future driving conditions. The simulation results in ADVISOR demonstrate that, under the conditions of various driving cycles, road slopes and vehicle parameters, the proposed strategy significantly improves fuel economy, which is very close to that of the optimal control based on Pontryagin's minimum principle, and greatly reduces computation complexity.展开更多
文摘This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.
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supported by the National Natural Science Foundation of China(61573090)the Research Funds for the Central Universities(N130108001)
文摘Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneousiy provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking (LQT) control method.
基金This work was supported by the National Basic Research Program of China (973 Program) under Grant No. 2007CB814904the Natural Science Foundation of China under Grant No. 10671112+1 种基金Shandong Province under Grant No. Z2006A01Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20060422018
文摘In this paper, tile authors first study two kinds of stochastic differential equations (SDEs) with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations (BSDEs) driven by Levy pro- cesses, the authors proceed to study a stochastic linear quadratic (LQ) optimal control problem with a Levy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results.
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.
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.
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 National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11231007,11301298,11471231,11401404,11371226,11071145 and 11231005)+2 种基金China Postdoctoral Science Foundation(Grant No.2014M562321)Foundation for Innovative Research Groups of National Natural Science Foundation of China(Grant No.11221061)the Program for Introducing Talents of Discipline to Universities(the National 111Project of China's Higher Education)(Grant No.B12023)
文摘This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different ways.As a consequence,the open problems raised by Chen and Yong(2007) are solved.To characterize the saddle points more clearly,coupled forward-backward stochastic Volterra integral equations and stochastic Fredholm-Volterra integral equations are introduced.Compared with deterministic game problems,some new terms arising from the procedure of deriving the later equations reflect well the essential nature of stochastic systems.Moreover,our representations and arguments are even new in the classical SDEs case.
文摘Abstract This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefficients, which is actually a control combining the H2 optimization with the H∞ robust performance as the name of H2/H∞ reveals. Based on the classical theory of linear-quadratic (LQ, for short) optimal control, the sufficient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation (BSRE, for short) associated with H∞ robustness are derived. Then the sufficient and necessary conditions for the existence of the H2/H∞ control are given utilizing a pair of coupled stochastic Pdccati equations.
文摘In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates(increases and decreases) between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related:after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.
文摘Energy management strategies based on optimal control theory can achieve minimum fuel consumption for hybrid electric vehicles, but the requirement for driving cycles known in prior leads to a real-time problem. A real-time optimization power-split strategy is proposed based on linear quadratic optimal control. The battery state of charge sustainability and fuel economy are ensured by designing a quadratic performance index combined with two rules. The engine power and motor power of this strategy are calculated in real-time based on current system state and command, and not related to future driving conditions. The simulation results in ADVISOR demonstrate that, under the conditions of various driving cycles, road slopes and vehicle parameters, the proposed strategy significantly improves fuel economy, which is very close to that of the optimal control based on Pontryagin's minimum principle, and greatly reduces computation complexity.