Optimal control approach to stability criteria on Hill's equations

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.

Optimal control of a quality supervision profit model for the electronic intermediary

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.

Optimal control of stretching process of flexible solar arrays on spacecraft based on a hybrid optimization strategy

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.

Start-up phase plasma discharge design of a tokamak via control parameterization method

The tokamak start-up is a very important phase during the process to obtain a suitable equalizing plasma, and its governing model can be described as a set of nonlinear ordinary differential equations（ODEs）. In this paper, we first estimate the parameters in the original model and set up an accurate model to express how the variables change during the start-up phase, especially how the plasma current changes with respect to time and the loop voltage. Then, we apply the control parameterization method to obtain an approximate optimal parameters selection problem for the loop voltage design to achieve a desired plasma current target. Computational optimal control techniques such as the variational method and the costate method are employed to solve the problem, respectively. Finally, numerical simulations are performed and the results obtained via different methods are compared. Our numerical parameterization method and optimization procedure turn out to be effective.

NEW OPTIMAL LARGE ANGLE MANEUVER STRATEGY FOR SINGLE FLEXIBLE LINK

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.

PREDICTION AND CONTROL OF BOTH WRINKLE AND FRACTURE LIMITS ON CYLINDRICAL CUP MULTI DEEP DRAWING

Based on the superfluous triangle material wrinkle model,the no wrinkle limit criterion of cylindrical cup multi deep drawing is calculated as the prediction and control of the wrinkle limit.According to fracture model,the no fracture limit criterion of cylindrical cup multi deep drawing is calculated as the prediction and control of the fracture limit.Combining the no wrinkle limit criterion with the no fracture limit criterion,the no wrinkle and no fracture limit criterion and diagram on cylindrecal cup multi deep drawing are given as the prediction and control of both wrinkle and fracture limits.In accordance with this can determine the limit deep drawing coefficient and minimum deep drawing coefficient,and can choose the deep drawing coefficient of multi deep drawing,blank holder force and deformation force by optimization choice method.Theory calculation and test data are highly consistent,and suitable for no flange multi deep drawing,flange multi deep drawing and rigid punch expanding

SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

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.

Prediction of pilot workload in helicopter landing after one engine failure

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.