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
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
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
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
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 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
In this paper,we study the linear quadratic(LQ)optimal control of time-varying difference system with terminal state constraints.The main contribution is to provide the Q-learning algorithm for the optimal controller ...In this paper,we study the linear quadratic(LQ)optimal control of time-varying difference system with terminal state constraints.The main contribution is to provide the Q-learning algorithm for the optimal controller under the case that the time-varying system matrices and input matrices are both unknown,which consists of learning the solution of the Riccati equation and calculating the specific Lagrange multiplier from the data-driven matrix equation.Different from the existing Q-learning algorithms that mainly focus on unconstrained optimal control problems,the novelty of the proposed algorithm can be applied to handle situations with terminal state constraints.The effectiveness of the proposed Q-learning algorithm is demonstrated through a numerical example.展开更多
Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better ...Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better than its nonmonotone variant.With the aim of shrinking the gap between theory and practice of nonmonotone gradient methods,we introduce a property for convergence analysis of a large collection of gradient methods.We prove that any gradient method using stepsizes satisfying the property will converge R-linearly at a rate of 1-λ_(1)/M_(1),whereλ_(1)is the smallest eigenvalue of Hessian matrix and M_(1)is the upper bound of the inverse stepsize.Our results indicate that the existing convergence rates of many nonmonotone methods can be improved to 1-1/κwithκbeing the associated condition number.展开更多
In this paper,the authors consider a class of linear quadratic optimal control problems of backward stochastic differential equations under partial information with initial value constraint.The main contribution is to...In this paper,the authors consider a class of linear quadratic optimal control problems of backward stochastic differential equations under partial information with initial value constraint.The main contribution is to obtain an explicitly optimal controller by using a Riccati equation and an optimal parameter characterized by a matrix equation.The key technique is to introduce Lagrange multiplier to transform the problem with initial value constraint into unconstrained optimal control problem and optimal parameter calculation problem,and solve the optimal parameter calculation by using the exact controllability of the system.展开更多
Buildings use a large amount of energy in the United States.It is important to optimally manage and coordinate the resources across building and power distribution networks to improve overall efficiency.Optimizing the...Buildings use a large amount of energy in the United States.It is important to optimally manage and coordinate the resources across building and power distribution networks to improve overall efficiency.Optimizing the power grid with discrete variables was very challenging for traditional computers and algorithms,as it is an NP-hard problem.In this study,we developed a new optimization solution based on quantum computing for BTG integration.We first used MPC for building loads connected with a commercial distribution grid for cost reduction.Then we used discretization and Benders Decomposition methods to reformulate the problem and decompose the continuous and discrete variables,respectively.We used D-Wave quantum computer to solve dual problems and used conventional algorithm for primal problems.We applied the proposed method to an IEEE 9-bus network with 3 commercial buildings and over 300 residential buildings to evaluate the feasibility and effectiveness.Compared with traditional optimization methods,we obtained similar solutions with some fluctuations and improved computational speed from hours to seconds.The time of quantum computing was greatly reduced to less than 1% of traditional optimization algorithm and software such as MATLAB.Quantum computing has proved the potential to solve large-scale discrete optimization problems for urban energy systems.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
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.
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.
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.
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.
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.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 Natural Science Foundation of Shandong Province(Nos.ZR2021ZD14,ZR2021JQ24,and ZR2024QF198).
文摘In this paper,we study the linear quadratic(LQ)optimal control of time-varying difference system with terminal state constraints.The main contribution is to provide the Q-learning algorithm for the optimal controller under the case that the time-varying system matrices and input matrices are both unknown,which consists of learning the solution of the Riccati equation and calculating the specific Lagrange multiplier from the data-driven matrix equation.Different from the existing Q-learning algorithms that mainly focus on unconstrained optimal control problems,the novelty of the proposed algorithm can be applied to handle situations with terminal state constraints.The effectiveness of the proposed Q-learning algorithm is demonstrated through a numerical example.
基金supported by the National Natural Science Foundation of China(No.11701137)the Natural Science Foundation of Hebei Province(No.A2021202010).
文摘Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better than its nonmonotone variant.With the aim of shrinking the gap between theory and practice of nonmonotone gradient methods,we introduce a property for convergence analysis of a large collection of gradient methods.We prove that any gradient method using stepsizes satisfying the property will converge R-linearly at a rate of 1-λ_(1)/M_(1),whereλ_(1)is the smallest eigenvalue of Hessian matrix and M_(1)is the upper bound of the inverse stepsize.Our results indicate that the existing convergence rates of many nonmonotone methods can be improved to 1-1/κwithκbeing the associated condition number.
基金supported by the Natural Science Foundation of Shandong Province under Grant Nos.ZR2021ZD14,ZR2021JQ24,and ZR2024QF198。
文摘In this paper,the authors consider a class of linear quadratic optimal control problems of backward stochastic differential equations under partial information with initial value constraint.The main contribution is to obtain an explicitly optimal controller by using a Riccati equation and an optimal parameter characterized by a matrix equation.The key technique is to introduce Lagrange multiplier to transform the problem with initial value constraint into unconstrained optimal control problem and optimal parameter calculation problem,and solve the optimal parameter calculation by using the exact controllability of the system.
基金supported by the Collaboration for Unprecedented Success and Excellence(CUSE)Grant at Syracuse University under Ⅱ-3267-2022by the U.S.National Science Foundation under Award No.1949372.
文摘Buildings use a large amount of energy in the United States.It is important to optimally manage and coordinate the resources across building and power distribution networks to improve overall efficiency.Optimizing the power grid with discrete variables was very challenging for traditional computers and algorithms,as it is an NP-hard problem.In this study,we developed a new optimization solution based on quantum computing for BTG integration.We first used MPC for building loads connected with a commercial distribution grid for cost reduction.Then we used discretization and Benders Decomposition methods to reformulate the problem and decompose the continuous and discrete variables,respectively.We used D-Wave quantum computer to solve dual problems and used conventional algorithm for primal problems.We applied the proposed method to an IEEE 9-bus network with 3 commercial buildings and over 300 residential buildings to evaluate the feasibility and effectiveness.Compared with traditional optimization methods,we obtained similar solutions with some fluctuations and improved computational speed from hours to seconds.The time of quantum computing was greatly reduced to less than 1% of traditional optimization algorithm and software such as MATLAB.Quantum computing has proved the potential to solve large-scale discrete optimization problems for urban energy systems.
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.
