This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods develo...This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov’s criterion, Neǐgauz and Lidskiǐ’s criterion. Secondly, we present stability criteria on Hill’s equations with sign-changing potential in which Brog’s criterion and Krein’s criterion are included.展开更多
The optimal control of multibody spacecraft during the stretching process of solar arrays is investigated,and a hybrid optimization strategy based on Gauss pseudospectral method（GPM） and direct shooting method（DSM...The optimal control of multibody spacecraft during the stretching process of solar arrays is investigated,and a hybrid optimization strategy based on Gauss pseudospectral method（GPM） and direct shooting method（DSM） is presented. First, the elastic deformation of flexible solar arrays was described approximately by the assumed mode method, and a dynamic model was established by the second Lagrangian equation. Then, the nonholonomic motion planning problem is transformed into a nonlinear programming problem by using GPM. By giving fewer LG points, initial values of the state variables and control variables were obtained. A serial optimization framework was adopted to obtain the approximate optimal solution from a feasible solution. Finally, the control variables were discretized at LG points, and the precise optimal control inputs were obtained by DSM. The optimal trajectory of the system can be obtained through numerical integration. Through numerical simulation, the stretching process of solar arrays is stable with no detours, and the control inputs match the various constraints of actual conditions.The results indicate that the method is effective with good robustness.展开更多
The paper focuses on the optimal control of natural resources in mining industry. The purpose is to pro- pose an optimal extraction series of these resources during the lifetime of the Mine＇s maintenance. Fol- lowing...The paper focuses on the optimal control of natural resources in mining industry. The purpose is to pro- pose an optimal extraction series of these resources during the lifetime of the Mine＇s maintenance. Fol- lowing the proposed optimal control model, a sensitivity analysis has been performed that includes the interest rate impact on the optimal solution. This study shows that the increasing of the interest rate sti- mulates faster extraction of the resources. The discounting factor induces that the resource has to be extracted faster hut this effect is counterbalanced by the diminishing returns of the annual cash flow. At higher parameters of ＂alpha＂ close to one of the power function about 80% from the whole resource will be extracted during the first 4 years of object/mine maintenance. An existence of unique positive root with respect to return of investment has been proposed and proved by two ways： by the ＂method of chords＂ and by using specialized software.展开更多
Online customers execute transactions without inspecting products could expect to encounter risks of receiving products with unsatisfactory qualities,especially in food trans-actions.Thus quality supervision plays a k...Online customers execute transactions without inspecting products could expect to encounter risks of receiving products with unsatisfactory qualities,especially in food trans-actions.Thus quality supervision plays a key role in the establishment of trust as well as in the management of risk between online customers and sellers.Most papers in this field are in qualitative nature.In this paper,a quality supervision profit(QSP)model is formulated as a discrete-time optimal control problem.It is a quantitative approach,and it broadens the scope.of current research in the area.The quality efort level of online sellers(QELa)and the quality supervision level of the electronic intermediary(QSLm)are considered together with their cor-responding profit in the proposed model.The aim is to optimize an overall profit.A case study arising from Suichang's food traceability system(FTS)of farm produce online transaction is carried out in details.The results reveal that QELs,QSLm and the profit distribution coeffi-cient have a strong influence upon the profits of both sides.Finally,some concluding remarks,including potential further research topics,are given.展开更多
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of ...The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.展开更多
This study aims to optimize the inbound traffic flow on on-ramps by considering low time costs,good speed stability,and high driving safety for mixed traffic flow.The optimal inlet gap is identified in advance,and tra...This study aims to optimize the inbound traffic flow on on-ramps by considering low time costs,good speed stability,and high driving safety for mixed traffic flow.The optimal inlet gap is identified in advance,and trajectory guidance for vehicles entering the gap is determined under safety constraints.Based on the initial state and sequence of vehicles entering the merging area,individual vehicle trajectories are optimized sequentially.An optimization model and method for ramp entry trajectories in mixed traffic flow are developed,incorporating on-ramp vehicle entry sequencing and ordinary vehicle trajectory prediction.Key performance indicators,including driving safety,total travel time,parking wait probability,and trajectory smoothness,are compared and analyzed to evaluate the proposed approach.展开更多
A component synthesis vibration suppression (CSVS) method for flexible structures is put forward. It can eliminate any unwanted orders of flexible vibration modes while achieves desired rigid motion. This method has ...A component synthesis vibration suppression (CSVS) method for flexible structures is put forward. It can eliminate any unwanted orders of flexible vibration modes while achieves desired rigid motion. This method has robustness to uncertainty of frequency, which makes it practical in engineering. Several time optimal and time-fuel optimal control strategies are designed for a kind of single flexible link. Simulation results validate the feasibility of our method.展开更多
This paper presents a method to predict the pilot workload in helicopter landing after one engine failure.The landing procedure is simulated numerically via applying nonlinear optimal control method in the form of per...This paper presents a method to predict the pilot workload in helicopter landing after one engine failure.The landing procedure is simulated numerically via applying nonlinear optimal control method in the form of performance index,path constraints and boundary conditions based on an augmented six-degree-of-freedom rigid-body flight dynamics model,solved by collocation and numerical optimization method.UH-60 A helicopter is taken as the sample for the demonstration of landing after one engine failure.The numerical simulation was conducted to find the trajectory of helicopter and the controls from pilot for landing after one engine failure with different performance index considering the factor of pilot workload.The reasonable performance index and corresponding landing trajectory and controls are obtained by making a comparison with those from the flight test data.Furthermore,the pilot workload is evaluated based on wavelet transform analysis of the pilot control activities.The workloads of pilot control activities for collective control,longitudinal and lateral cyclic controls and pedal control during the helicopter landing after one engine failure are examined and compared with those of flight test.The results show that when the performance index considers the factor of pilot workload properly,the characteristics of amplitudes and constituent frequencies of pilot control inputs in the optimal solution are consistent with those of the pilot control inputs in the flight test.Therefore,the proposed method provides a tool of predicting the pilot workload in helicopter landing after one engine failure.展开更多
In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an a...In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.展开更多
基金supported by NSFC(11401089,11671071)the Scientific Technological Project of Jilin Province’s Education Department in Thirteenth Five-Year(JJKH20170535KJ)+1 种基金supported by NSFC(11571065)the National Basic Research Program of China(2013CB834102)
文摘This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov’s criterion, Neǐgauz and Lidskiǐ’s criterion. Secondly, we present stability criteria on Hill’s equations with sign-changing potential in which Brog’s criterion and Krein’s criterion are included.
基金supported by the National Natural Science Foundation of China (11472058)
文摘The optimal control of multibody spacecraft during the stretching process of solar arrays is investigated,and a hybrid optimization strategy based on Gauss pseudospectral method（GPM） and direct shooting method（DSM） is presented. First, the elastic deformation of flexible solar arrays was described approximately by the assumed mode method, and a dynamic model was established by the second Lagrangian equation. Then, the nonholonomic motion planning problem is transformed into a nonlinear programming problem by using GPM. By giving fewer LG points, initial values of the state variables and control variables were obtained. A serial optimization framework was adopted to obtain the approximate optimal solution from a feasible solution. Finally, the control variables were discretized at LG points, and the precise optimal control inputs were obtained by DSM. The optimal trajectory of the system can be obtained through numerical integration. Through numerical simulation, the stretching process of solar arrays is stable with no detours, and the control inputs match the various constraints of actual conditions.The results indicate that the method is effective with good robustness.
文摘The paper focuses on the optimal control of natural resources in mining industry. The purpose is to pro- pose an optimal extraction series of these resources during the lifetime of the Mine＇s maintenance. Fol- lowing the proposed optimal control model, a sensitivity analysis has been performed that includes the interest rate impact on the optimal solution. This study shows that the increasing of the interest rate sti- mulates faster extraction of the resources. The discounting factor induces that the resource has to be extracted faster hut this effect is counterbalanced by the diminishing returns of the annual cash flow. At higher parameters of ＂alpha＂ close to one of the power function about 80% from the whole resource will be extracted during the first 4 years of object/mine maintenance. An existence of unique positive root with respect to return of investment has been proposed and proved by two ways： by the ＂method of chords＂ and by using specialized software.
基金Supported by Zhejiang Provincial basic public welfare research project of China(LGN19C040001)。
文摘Online customers execute transactions without inspecting products could expect to encounter risks of receiving products with unsatisfactory qualities,especially in food trans-actions.Thus quality supervision plays a key role in the establishment of trust as well as in the management of risk between online customers and sellers.Most papers in this field are in qualitative nature.In this paper,a quality supervision profit(QSP)model is formulated as a discrete-time optimal control problem.It is a quantitative approach,and it broadens the scope.of current research in the area.The quality efort level of online sellers(QELa)and the quality supervision level of the electronic intermediary(QSLm)are considered together with their cor-responding profit in the proposed model.The aim is to optimize an overall profit.A case study arising from Suichang's food traceability system(FTS)of farm produce online transaction is carried out in details.The results reveal that QELs,QSLm and the profit distribution coeffi-cient have a strong influence upon the profits of both sides.Finally,some concluding remarks,including potential further research topics,are given.
文摘The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.
文摘This study aims to optimize the inbound traffic flow on on-ramps by considering low time costs,good speed stability,and high driving safety for mixed traffic flow.The optimal inlet gap is identified in advance,and trajectory guidance for vehicles entering the gap is determined under safety constraints.Based on the initial state and sequence of vehicles entering the merging area,individual vehicle trajectories are optimized sequentially.An optimization model and method for ramp entry trajectories in mixed traffic flow are developed,incorporating on-ramp vehicle entry sequencing and ordinary vehicle trajectory prediction.Key performance indicators,including driving safety,total travel time,parking wait probability,and trajectory smoothness,are compared and analyzed to evaluate the proposed approach.
基金This project is supported by National 211 Project.
文摘A component synthesis vibration suppression (CSVS) method for flexible structures is put forward. It can eliminate any unwanted orders of flexible vibration modes while achieves desired rigid motion. This method has robustness to uncertainty of frequency, which makes it practical in engineering. Several time optimal and time-fuel optimal control strategies are designed for a kind of single flexible link. Simulation results validate the feasibility of our method.
基金supported by the National Natural Science Foundation of China(No.11672128)。
文摘This paper presents a method to predict the pilot workload in helicopter landing after one engine failure.The landing procedure is simulated numerically via applying nonlinear optimal control method in the form of performance index,path constraints and boundary conditions based on an augmented six-degree-of-freedom rigid-body flight dynamics model,solved by collocation and numerical optimization method.UH-60 A helicopter is taken as the sample for the demonstration of landing after one engine failure.The numerical simulation was conducted to find the trajectory of helicopter and the controls from pilot for landing after one engine failure with different performance index considering the factor of pilot workload.The reasonable performance index and corresponding landing trajectory and controls are obtained by making a comparison with those from the flight test data.Furthermore,the pilot workload is evaluated based on wavelet transform analysis of the pilot control activities.The workloads of pilot control activities for collective control,longitudinal and lateral cyclic controls and pedal control during the helicopter landing after one engine failure are examined and compared with those of flight test.The results show that when the performance index considers the factor of pilot workload properly,the characteristics of amplitudes and constituent frequencies of pilot control inputs in the optimal solution are consistent with those of the pilot control inputs in the flight test.Therefore,the proposed method provides a tool of predicting the pilot workload in helicopter landing after one engine failure.
文摘In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.
