In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These ...In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method （IPM） to O（√n log nlog n/e）, which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter.展开更多
In order that the mechanism designed meets the requirements of kinematics with optimal dynamics behaviors, a quadratic optimization method is proposed based on the different characteristics of kinematic and dynamic op...In order that the mechanism designed meets the requirements of kinematics with optimal dynamics behaviors, a quadratic optimization method is proposed based on the different characteristics of kinematic and dynamic optimization. This method includes two steps of optimization, that is, kinematic and dynamic optimization. Meanwhile, it uses the results of the kinematic optimization as the constraint equations of dynamic optimization. This method is used in the parameters optimization of transplanting mechanism with elliptic planetary gears of high-speed rice seedling transplanter with remarkable significance. The parameters spectrum, which meets to the kinematic requirements, is obtained through visualized human-computer interactions in the kinematics optimization, and the optimal parameters are obtained based on improved genetic algorithm in dynamic optimization. In the dynamic optimization, the objective function is chosen as the optimal＇ dynamic behavior and the constraint equations are from the results of the kinematic optimization, This method is suitable for multi-objective optimization when both the kinematic and dynamic performances act as objective functions.展开更多
This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method fo...This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.展开更多
As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and soluti...As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and solution optimality.To tackle this issue,we propose a problem-structure-informed quantum approximate optimization algorithm(QAOA)framework that fully exploits the quantum advantage under extremely limited quantum resources.Specifically,we leverage the inherent topological structure of power systems to decompose large-scale UCP instances into smaller subproblems,which are solvable in parallel by limited number of qubits.This decomposition not only circumvents the current hardware limitations of quantum computing but also achieves higher performance as the graph structure of the power system becomes more sparse.Consequently,our approach can be extended to future power systems that are larger and more complex.展开更多
The Robogymnast is a triple link underactuated pendulum that mimics a human gymnast hanging from a horizontal bar.In this paper, two multi-objective optimization methods are developed using invasive weed optimization...The Robogymnast is a triple link underactuated pendulum that mimics a human gymnast hanging from a horizontal bar.In this paper, two multi-objective optimization methods are developed using invasive weed optimization（IWO）. The first method is the weighted criteria method IWO（WCMIWO） and the second method is the fuzzy logic IWO hybrid（FLIWOH）. The two optimization methods were used to investigate the optimum diagonal values for the Q matrix of the linear quadratic regulator（LQR） controller that can balance the Robogymnast in an upright configuration. Two LQR controllers were first developed using the parameters obtained from the two optimization methods. The same process was then repeated, but this time with disturbance applied to the Robogymnast states to develop another set of two LQR controllers. The response of the controllers was then tested in different scenarios using simulation and their performance evaluated. The results show that all four controllers are able to balance the Robogymnast with varying accuracies. It has also been observed that the controllers trained with disturbance achieve faster settling time.展开更多
A novel iterative technique, the phase descent search detection was proposed. This technique constrained the solution （PDS） algorithm, for M-ary phase shift keying （M-PSK） symbols to have a unit magnitude and it w...A novel iterative technique, the phase descent search detection was proposed. This technique constrained the solution （PDS） algorithm, for M-ary phase shift keying （M-PSK） symbols to have a unit magnitude and it was based on coordinate descent iterations where coordinates were the unknown symbol phases. The PDS algorithm, together with a descent local search （also implemented as a version of the PDS algorithm）, was used multiple times with different initializations in a proposed multiple phase detector; the solution with the minimum cost was then chosen as the final solution. The simulation results show that for highly loaded multiuser scenarios, the proposed technique has a detection performance that is close to the single-user bound. The results also show that the multiple phase detector allows detection in highly overloaded scenarios and it exhibits near-far resistance. In particular, the detector has a performance that is significantly better, and complexity that is significantly lower, than that of the detector based on semi-definite relaxation.展开更多
This paper explores related aspects to post-Pareto analysis arising from the multicriteria optimization problem.It consists of two main parts.In the first one,we give first-order necessary optimality conditions for a ...This paper explores related aspects to post-Pareto analysis arising from the multicriteria optimization problem.It consists of two main parts.In the first one,we give first-order necessary optimality conditions for a semi-vectorial bi-level optimization problem:the upper level is a scalar optimization problem to be solved by the leader,and the lower level is a multi-objective optimization problem to be solved by several followers acting in a cooperative way(greatest coalition multi-players game).For the lower level,we deal with weakly or properly Pareto(efficient)solutions and we consider the so-called optimistic problem,i.e.when followers choose amongst Pareto solutions one which is the most favourable for the leader.In order to handle reallife applications,in the second part of the paper,we consider the case where each follower objective is expressed in a quadratic form.In this setting,we give explicit first-order necessary optimality conditions.Finally,some computational results are given to illustrate the paper.展开更多
In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular functi...In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be O（√n（logn）2 log e/n）. This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and in optimization fields. Some computational results recent kernel functions introduced by some authors have been provided.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
For a given set of data points in the plane, a new method is presented for computing a parameter value（knot） for each data point. Associated with each data point, a quadratic polynomial curve passing through three a...For a given set of data points in the plane, a new method is presented for computing a parameter value（knot） for each data point. Associated with each data point, a quadratic polynomial curve passing through three adjacent consecutive data points is constructed. The curve has one degree of freedom which can be used to optimize the shape of the curve. To obtain a better shape of the curve, the degree of freedom is determined by optimizing the bending and stretching energies of the curve so that variation of the curve is as small as possible. Between each pair of adjacent data points, two local knot intervals are constructed, and the final knot interval corresponding to these two points is determined by a combination of the two local knot intervals. Experiments show that the curves constructed using the knots by the new method generally have better interpolation precision than the ones constructed using the knots by the existing local methods.展开更多
In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the converg...In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the convergence analysis and obtain the polynomial complexity bound of the proposed algorithm.Although the algorithm belongs to the class of large-step interior-point algorithms,its complexity coincides with the best iteration bound for short-step interior-point algorithms.The algorithm is also implemented to demonstrate that it is efficient.展开更多
This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)...This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)framework.For the MFS control problem,this review discusses the existing conclusions on optimization in dynamic systems affected by both additive and multiplicative noises.In exploring MFT optimization,the authors first revisit researches associated with single-player systems constrained by these dynamics.The authors then extend the proposed review to scenarios that include multiple players engaged in Nash games,Stackelberg games,and cooperative Pareto games.Finally,the paper concludes by emphasizing future research on intelligent algorithms for mean field optimization,particularly using reinforcement learning method to design strategies for models with unknown parameters.展开更多
In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this...In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this framework,in contrast to the classical LQ issue,embodies that the admissible control set needs to satisfy more than the square integrability.By introducing two kinds of new generalized Riccati equations,we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation.A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited.Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized,and associated efficient portfolios are given in a closed form.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
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
This paper considers the fully coupled forward-backward stochastic functional differential equations(FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated ...This paper considers the fully coupled forward-backward stochastic functional differential equations(FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward stochastic differential equations as the backward equations. The authors will prove the existence and uniqueness theorem for FBSFDEs. As an application, we deal with a quadratic optimal control problem for functional stochastic systems, and get the explicit form of the optimal control by virtue of FBSFDEs.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
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
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
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
基金the Foundation of Scientific Research for Selecting and Cultivating Young Excellent University Teachers in Shanghai (Grant No.06XPYQ52)the Shanghai Pujiang Program (Grant No.06PJ14039)
文摘In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method （IPM） to O（√n log nlog n/e）, which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter.
基金This project is supported by National Natural Science Foundation of China (No.50275137)Basic Research Major Project of China Science and Technology Ministry(No.2004CCA05700)Provincial Natural Science Foundation of Zhejiang, China (No. Z105706).
文摘In order that the mechanism designed meets the requirements of kinematics with optimal dynamics behaviors, a quadratic optimization method is proposed based on the different characteristics of kinematic and dynamic optimization. This method includes two steps of optimization, that is, kinematic and dynamic optimization. Meanwhile, it uses the results of the kinematic optimization as the constraint equations of dynamic optimization. This method is used in the parameters optimization of transplanting mechanism with elliptic planetary gears of high-speed rice seedling transplanter with remarkable significance. The parameters spectrum, which meets to the kinematic requirements, is obtained through visualized human-computer interactions in the kinematics optimization, and the optimal parameters are obtained based on improved genetic algorithm in dynamic optimization. In the dynamic optimization, the objective function is chosen as the optimal＇ dynamic behavior and the constraint equations are from the results of the kinematic optimization, This method is suitable for multi-objective optimization when both the kinematic and dynamic performances act as objective functions.
基金supported by the National Natural Science Foundation of China(12171106)the Natural Science Foundation of Guangxi Province(2020GXNSFDA238017 and 2018GXNSFFA281007)the Shanghai Sailing Program(21YF1430300)。
文摘This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.
文摘As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and solution optimality.To tackle this issue,we propose a problem-structure-informed quantum approximate optimization algorithm(QAOA)framework that fully exploits the quantum advantage under extremely limited quantum resources.Specifically,we leverage the inherent topological structure of power systems to decompose large-scale UCP instances into smaller subproblems,which are solvable in parallel by limited number of qubits.This decomposition not only circumvents the current hardware limitations of quantum computing but also achieves higher performance as the graph structure of the power system becomes more sparse.Consequently,our approach can be extended to future power systems that are larger and more complex.
基金Majlis Amanah Rakyat (MARA)German Malaysian Institute (GMI) for their sponsorship
文摘The Robogymnast is a triple link underactuated pendulum that mimics a human gymnast hanging from a horizontal bar.In this paper, two multi-objective optimization methods are developed using invasive weed optimization（IWO）. The first method is the weighted criteria method IWO（WCMIWO） and the second method is the fuzzy logic IWO hybrid（FLIWOH）. The two optimization methods were used to investigate the optimum diagonal values for the Q matrix of the linear quadratic regulator（LQR） controller that can balance the Robogymnast in an upright configuration. Two LQR controllers were first developed using the parameters obtained from the two optimization methods. The same process was then repeated, but this time with disturbance applied to the Robogymnast states to develop another set of two LQR controllers. The response of the controllers was then tested in different scenarios using simulation and their performance evaluated. The results show that all four controllers are able to balance the Robogymnast with varying accuracies. It has also been observed that the controllers trained with disturbance achieve faster settling time.
文摘A novel iterative technique, the phase descent search detection was proposed. This technique constrained the solution （PDS） algorithm, for M-ary phase shift keying （M-PSK） symbols to have a unit magnitude and it was based on coordinate descent iterations where coordinates were the unknown symbol phases. The PDS algorithm, together with a descent local search （also implemented as a version of the PDS algorithm）, was used multiple times with different initializations in a proposed multiple phase detector; the solution with the minimum cost was then chosen as the final solution. The simulation results show that for highly loaded multiuser scenarios, the proposed technique has a detection performance that is close to the single-user bound. The results also show that the multiple phase detector allows detection in highly overloaded scenarios and it exhibits near-far resistance. In particular, the detector has a performance that is significantly better, and complexity that is significantly lower, than that of the detector based on semi-definite relaxation.
文摘This paper explores related aspects to post-Pareto analysis arising from the multicriteria optimization problem.It consists of two main parts.In the first one,we give first-order necessary optimality conditions for a semi-vectorial bi-level optimization problem:the upper level is a scalar optimization problem to be solved by the leader,and the lower level is a multi-objective optimization problem to be solved by several followers acting in a cooperative way(greatest coalition multi-players game).For the lower level,we deal with weakly or properly Pareto(efficient)solutions and we consider the so-called optimistic problem,i.e.when followers choose amongst Pareto solutions one which is the most favourable for the leader.In order to handle reallife applications,in the second part of the paper,we consider the case where each follower objective is expressed in a quadratic form.In this setting,we give explicit first-order necessary optimality conditions.Finally,some computational results are given to illustrate the paper.
基金Supported by Natural Science Foundation of Hubei Province of China (Grant No. 2008CDZ047)
文摘In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be O（√n（logn）2 log e/n）. This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and in optimization fields. Some computational results recent kernel functions introduced by some authors have been provided.
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Supported by the National Natural Science Foundation of China(61602277,61672327,61472227)the Shandong Provincial Natural Science Foundation,China(ZR2016FQ12)
文摘For a given set of data points in the plane, a new method is presented for computing a parameter value（knot） for each data point. Associated with each data point, a quadratic polynomial curve passing through three adjacent consecutive data points is constructed. The curve has one degree of freedom which can be used to optimize the shape of the curve. To obtain a better shape of the curve, the degree of freedom is determined by optimizing the bending and stretching energies of the curve so that variation of the curve is as small as possible. Between each pair of adjacent data points, two local knot intervals are constructed, and the final knot interval corresponding to these two points is determined by a combination of the two local knot intervals. Experiments show that the curves constructed using the knots by the new method generally have better interpolation precision than the ones constructed using the knots by the existing local methods.
文摘In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the convergence analysis and obtain the polynomial complexity bound of the proposed algorithm.Although the algorithm belongs to the class of large-step interior-point algorithms,its complexity coincides with the best iteration bound for short-step interior-point algorithms.The algorithm is also implemented to demonstrate that it is efficient.
基金supported by the National Natural Science Foundation of China under Grant Nos.62103442,12326343,62373229the Research Grants Council of the Hong Kong Special Administrative Region,China under Grant Nos.CityU 11213023,11205724+3 种基金the Natural Science Foundation of Shandong Province under Grant No.ZR2021QF080the Taishan Scholar Project of Shandong Province under Grant No.tsqn202408110the Fundamental Research Foundation of the Central Universities under Grant No.23CX06024Athe Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant No.2023KJ061.
文摘This paper reviews the mean field social(MFS)optimal control problem for multi-agent dynamic systems and the mean-field-type(MFT)optimal control problem for single-agent dynamic systems within the linear quadratic(LQ)framework.For the MFS control problem,this review discusses the existing conclusions on optimization in dynamic systems affected by both additive and multiplicative noises.In exploring MFT optimization,the authors first revisit researches associated with single-player systems constrained by these dynamics.The authors then extend the proposed review to scenarios that include multiple players engaged in Nash games,Stackelberg games,and cooperative Pareto games.Finally,the paper concludes by emphasizing future research on intelligent algorithms for mean field optimization,particularly using reinforcement learning method to design strategies for models with unknown parameters.
基金financial support partly by the National Nature Science Foundation of China(Grant No.12171053,11701040,11871010&61871058)the Fundamental Research Funds for the Central Universities+2 种基金the Research Funds of Renmin University of China(No.23XNKJ05)the financial support partly by the National Nature Science Foundation of China(Grant No.11871010,11971040)the Fundamental Research Funds for the Central Universities(No.2019XD-A11).
文摘In this paper,we focus on a control-constrained stochastic LQ optimal control problem via backward stochastic differential equation(BSDE in short)with deterministic coefficients.One of the significant features in this framework,in contrast to the classical LQ issue,embodies that the admissible control set needs to satisfy more than the square integrability.By introducing two kinds of new generalized Riccati equations,we are able to announce the explicit optimal control and the solution to the corresponding H-J-B equation.A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result with short-selling prohibited.Feasibility of the mean-variance portfolio selection problem via BSDE for a financial market is characterized,and associated efficient portfolios are given in a closed form.
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.
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the Program of Natural Science Research of Jiangsu Higher Education Institutions of China under Grant No. 17KJB110009。
文摘This paper considers the fully coupled forward-backward stochastic functional differential equations(FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward stochastic differential equations as the backward equations. The authors will prove the existence and uniqueness theorem for FBSFDEs. As an application, we deal with a quadratic optimal control problem for functional stochastic systems, and get the explicit form of the optimal control by virtue of FBSFDEs.
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.
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.
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.
