This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution ...This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.展开更多
In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain a...In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.展开更多
In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various...In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.展开更多
This paper concerns the weak solutions of some Monge-Amp^re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere typ...This paper concerns the weak solutions of some Monge-Amp^re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.展开更多
A multi-objective optimal operation model of water-sedimentation-power in reservoir is established with power-generation, sedimentation and water storage taken into account. Moreover, the inertia weight self-adjusting...A multi-objective optimal operation model of water-sedimentation-power in reservoir is established with power-generation, sedimentation and water storage taken into account. Moreover, the inertia weight self-adjusting mechanism and Pareto-optimal archive are introduced into the particle swarm optimization and an improved multi-objective particle swarm optimization （IMOPSO） is proposed. The IMOPSO is employed to solve the optimal model and obtain the Pareto-optimal front. The multi-objective optimal operation of Wanjiazhai Reservoir during the spring breakup was investigated with three typical flood hydrographs. The results show that the former method is able to obtain the Pareto-optimal front with a uniform distribution property. Different regions （A, B, C） of the Pareto-optimal front correspond to the optimized schemes in terms of the objectives of sediment deposition, sediment deposition and power generation, and power generation, respectively. The level hydrographs and outflow hydrographs show the operation of the reservoir in details. Compared with the non-dominated sorting genetic algorithm-Ⅱ （NSGA-Ⅱ）, IMOPSO has close global optimization capability and is suitable for multi-objective optimization problems.展开更多
To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-...To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.展开更多
Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alter...Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alternating projection algorithm to compute the optimal approximate symmetric positive semidefinite solution of the matrix equations AXB = E, CXD = F. If we choose the initial iterative matrix X<sub>0</sub> = 0, the least Frobenius norm symmetric positive semidefinite solution of these matrix equations is obtained. A numerical example shows that the new algorithm is feasible and effective.展开更多
In this paper, we have used two reliable approaches (theorems) to find the optimal solutions to transportation problems, using variations in costs. In real-life scenarios, transportation costs can fluctuate due to dif...In this paper, we have used two reliable approaches (theorems) to find the optimal solutions to transportation problems, using variations in costs. In real-life scenarios, transportation costs can fluctuate due to different factors. Finding optimal solutions to the transportation problem in the context of variations in cost is vital for ensuring cost efficiency, resource allocation, customer satisfaction, competitive advantage, environmental responsibility, risk mitigation, and operational fortitude in practical situations. This paper opens up new directions for the solution of transportation problems by introducing two key theorems. By using these theorems, we can develop an algorithm for identifying the optimal solution attributes and permitting accurate quantification of changes in overall transportation costs through the addition or subtraction of constants to specific rows or columns, as well as multiplication by constants inside the cost matrix. It is anticipated that the two reliable techniques presented in this study will provide theoretical insights and practical solutions to enhance the efficiency and cost-effectiveness of transportation systems. Finally, numerical illustrations are presented to verify the proposed approaches.展开更多
The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the pro...The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.展开更多
In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, t...In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.展开更多
The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the...The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.展开更多
This paper proposes an efficient method for optimal power flow solution （OPF） using particle swarm optimization （PSO） technique. The objective of the proposed method is to find the steady state operation point in ...This paper proposes an efficient method for optimal power flow solution （OPF） using particle swarm optimization （PSO） technique. The objective of the proposed method is to find the steady state operation point in a power system which minimizes the fuel cost, while maintaining an acceptable system performance in terms of limits on generator power, line flow limits and voltage limits. In order to improvise the performance of the conventional PSO （cPSO）, the fine tuning parameters- the inertia weight and acceleration coefficients are formulated in terms of global-local best values of the objective function. These global-local best inertia weight （GLBestlW） and global-local best acceleration coefficient （GLBestAC） are incorporated into PSO in order to compute the optimal power flow solution. The proposed method has been tested on the standard IEEE 30 bus test system to prove its efficacy. The results are compared with those obtained through cPSO. It is observed that the proposed algorithm is computationally faster, in terms of the number of load flows executed and provides better results than the conventional heuristic techniques.展开更多
With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions ...With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.展开更多
This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for...This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.展开更多
When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Li...When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.展开更多
We prove that the model with physical and human capital adjustment costs has optimal solution when the production function is increasing return and the structure of vetor fields of the model changes substantially when...We prove that the model with physical and human capital adjustment costs has optimal solution when the production function is increasing return and the structure of vetor fields of the model changes substantially when the prodution function from decreasing return turns to increasing return.And it is shown that the economy is improved when the coefficients of adjustment costs become small.展开更多
In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model w...In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.展开更多
The structure of the optimal solution set is derived for linear fractional programming with the representation theorem of polyhedral sets. Based on an adaptation of the convex simplex method credited to Gilmore and Go...The structure of the optimal solution set is derived for linear fractional programming with the representation theorem of polyhedral sets. Based on an adaptation of the convex simplex method credited to Gilmore and Gomory, we give the uniqueness condition of optimal solution and the computational procedures to find all optimal solutions if the uniqueness condition is not satisfied. Finally, an illustrative example is also given.展开更多
In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical...In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.展开更多
A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric varia...A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.展开更多
基金supported by the Anhui Provincial Natural Science Foundation(2408085QA031)the third author's work was supported by the National Natural Science Foundation of China(12001033).
文摘This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.
文摘In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.
基金Supported by the Natural Science Foundation of Zhejiang Province(LY21A010021)the National Natural Science Foundation of China(11701506)。
文摘In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.
基金supported by National Natural Science Foundation of China(11071119)
文摘This paper concerns the weak solutions of some Monge-Amp^re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.
基金National Science Fund for Distinguished Young Scholars (No.50725929)National Natural Science Foundation ofChina (No.50539060,50679052)
文摘A multi-objective optimal operation model of water-sedimentation-power in reservoir is established with power-generation, sedimentation and water storage taken into account. Moreover, the inertia weight self-adjusting mechanism and Pareto-optimal archive are introduced into the particle swarm optimization and an improved multi-objective particle swarm optimization （IMOPSO） is proposed. The IMOPSO is employed to solve the optimal model and obtain the Pareto-optimal front. The multi-objective optimal operation of Wanjiazhai Reservoir during the spring breakup was investigated with three typical flood hydrographs. The results show that the former method is able to obtain the Pareto-optimal front with a uniform distribution property. Different regions （A, B, C） of the Pareto-optimal front correspond to the optimized schemes in terms of the objectives of sediment deposition, sediment deposition and power generation, and power generation, respectively. The level hydrographs and outflow hydrographs show the operation of the reservoir in details. Compared with the non-dominated sorting genetic algorithm-Ⅱ （NSGA-Ⅱ）, IMOPSO has close global optimization capability and is suitable for multi-objective optimization problems.
基金Supported by the National Natural Science Foundation of China(10571141,70971109)the Key Projectof the National Natural Science Foundation of China(70531030)
文摘To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.
文摘Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alternating projection algorithm to compute the optimal approximate symmetric positive semidefinite solution of the matrix equations AXB = E, CXD = F. If we choose the initial iterative matrix X<sub>0</sub> = 0, the least Frobenius norm symmetric positive semidefinite solution of these matrix equations is obtained. A numerical example shows that the new algorithm is feasible and effective.
文摘In this paper, we have used two reliable approaches (theorems) to find the optimal solutions to transportation problems, using variations in costs. In real-life scenarios, transportation costs can fluctuate due to different factors. Finding optimal solutions to the transportation problem in the context of variations in cost is vital for ensuring cost efficiency, resource allocation, customer satisfaction, competitive advantage, environmental responsibility, risk mitigation, and operational fortitude in practical situations. This paper opens up new directions for the solution of transportation problems by introducing two key theorems. By using these theorems, we can develop an algorithm for identifying the optimal solution attributes and permitting accurate quantification of changes in overall transportation costs through the addition or subtraction of constants to specific rows or columns, as well as multiplication by constants inside the cost matrix. It is anticipated that the two reliable techniques presented in this study will provide theoretical insights and practical solutions to enhance the efficiency and cost-effectiveness of transportation systems. Finally, numerical illustrations are presented to verify the proposed approaches.
文摘The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.
基金Supported by the Research Foundation of Jinan University(04SKZD01).
文摘In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11075055 and 11275072)the Innovative Research Team Program of the National Natural Science Foundation of China(Grant No.61021004)+1 种基金the National High Technology Research and Development Program of China(Grant No.2011AA010101)the Shanghai Knowledge Service Platform for Trustworthy Internet of Things,China(Grant No.ZF1213)
文摘The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.
文摘This paper proposes an efficient method for optimal power flow solution （OPF） using particle swarm optimization （PSO） technique. The objective of the proposed method is to find the steady state operation point in a power system which minimizes the fuel cost, while maintaining an acceptable system performance in terms of limits on generator power, line flow limits and voltage limits. In order to improvise the performance of the conventional PSO （cPSO）, the fine tuning parameters- the inertia weight and acceleration coefficients are formulated in terms of global-local best values of the objective function. These global-local best inertia weight （GLBestlW） and global-local best acceleration coefficient （GLBestAC） are incorporated into PSO in order to compute the optimal power flow solution. The proposed method has been tested on the standard IEEE 30 bus test system to prove its efficacy. The results are compared with those obtained through cPSO. It is observed that the proposed algorithm is computationally faster, in terms of the number of load flows executed and provides better results than the conventional heuristic techniques.
文摘With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.
基金Supported by the National Natural Science Foundation of China（10871216） Supported by the Science and Technology Research Project of Chongqing Municipal Education Commission（KJ100419） Supported by the Natural Science Foundation Project of CQ CSTC（cstcjjA00019）
文摘This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.
基金Supported by the National Natural Science Foundation of China(10571141,70971109,71371152)supported by the Talents Fund of Xi’an Polytechnic University(BS1320)the Mathematics Discipline Development Fund of Xi’an Ploytechnic University(107090701)
文摘When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.
基金Supported by the Nationel Natural Science Foundation of China(79970104)
文摘We prove that the model with physical and human capital adjustment costs has optimal solution when the production function is increasing return and the structure of vetor fields of the model changes substantially when the prodution function from decreasing return turns to increasing return.And it is shown that the economy is improved when the coefficients of adjustment costs become small.
文摘In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.
文摘The structure of the optimal solution set is derived for linear fractional programming with the representation theorem of polyhedral sets. Based on an adaptation of the convex simplex method credited to Gilmore and Gomory, we give the uniqueness condition of optimal solution and the computational procedures to find all optimal solutions if the uniqueness condition is not satisfied. Finally, an illustrative example is also given.
文摘In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.
基金supported by the National Natural Science Foundation of China(Nos.11102031 and 11272076)the Fundamental Research Funds for Central Universities(No.DUT13LK25)+2 种基金the Key Laboratory Fund of Liaoning Province(No.L2013015)the China Postdoctoral Science Foundation(No.2014M550155)the State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-0114G02)
文摘A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.
