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INDEFINITE STOCHASTIC LQ CONTROL WITH CROSS TERM VIA SEMIDEFINITE PROGRAMMING
Luo, Chengxin,Feng, Enmin 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.13 No.1
An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.
Li, Kezan,Feng, Enmin,Xiu, Zhilong 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
According to the controllability of pulse times and the amount of jumps in the states at these times in the process of fed-batch culture producing 1,3-propanediol, this paper proposes a terminal optimal control model, whose constraint condition is the nonlinear impulsive delay system. The existence of optimal control is discussed and an optimization algorithm which is applied to each subinternal over one cycle for this optimal control problem is constructed. Finally, the numerical simulations show that the terminal intensity of producing 1,3-propanediol has been increased obviously.
STABILITY OF IMPULSIVE CONTROL SYSTEMS WITH VARIABLE TIMES
Zhao, Haiqing,Feng, Enmin 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
In this paper, cone-valued Lyapunov functions are employed to study the impulsive control system with variable times. The stability criteria on the non-zero solution of the impulsive control system are given by the cone-valued Lyapunov functions and the results of the controllability on the control system are also obtained.
AN APPROXIMATE GREEDY ALGORITHM FOR TAGSNP SELECTION USING LINKAGE DISEQUILIBRIUM CRITERIA
Wang, Ying,Feng, Enmin,Wang, Ruisheng Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
In this paper, we first construct a mathematical model for tagSNP selection based on LD measure $r^2$, then aiming at this kind of model, we develop an efficient algorithm, which is called approximate greedy algorithm. This algorithm is able to make up the disadvantage of the greedy algorithm for tagSNP selection. The key improvement of our approximate algorithm over greedy algorithm lies in that it adds local replacement(or local search) into the greedy search, tagSNP is replaced with the other SNP having greater similarity degree with it, and the local replacement is performed several times for a tagSNP so that it can improve the tagSNP set of the local precinct, thereby improve tagSNP set of whole precinct. The computational results prove that our approximate greedy algorithm can always find more efficient solutions than greedy algorithm, and improve the tagSNP set of whole precinct indeed.
Joint Estimation in Batch Culture by Using Unscented Kalman Filter
Xi Zhu,Enmin Feng 한국생물공학회 2012 Biotechnology and Bioprocess Engineering Vol.17 No.6
The disturbances caused by uncertain factors are inevitable in microbial fermentation. In this paper, we study the joint estimation problem for state and parameter in the bio-dissimulation process of glycerol to 1,3-PD in batch culture. Based on the nonlinear stochastic dynamic system model, we establish the corresponding iteration equations of Joint Unscented Kalman Filter (UKF) by referring to the Extended Kalman Filter (EKF), which is generally applied in microbial fermentation. Through numerical computation, both the state estimations and the uncertain model parameter estimations are obtained. Furthermore, the results of different parameter identification methods are compared. The results show that Joint UKF is more feasible for the process of controlling the glycerol fermentation. The disturbances caused by uncertain factors are inevitable in microbial fermentation. In this paper, we study the joint estimation problem for state and parameter in the bio-dissimulation process of glycerol to 1,3-PD in batch culture. Based on the nonlinear stochastic dynamic system model, we establish the corresponding iteration equations of Joint Unscented Kalman Filter (UKF) by referring to the Extended Kalman Filter (EKF), which is generally applied in microbial fermentation. Through numerical computation, both the state estimations and the uncertain model parameter estimations are obtained. Furthermore, the results of different parameter identification methods are compared. The results show that Joint UKF is more feasible for the process of controlling the glycerol fermentation.
Stability of impulsive control systems \\ with variable times
HAIQING ZHAO,ENMIN FENG 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
In this paper, cone-valued Lyapunov functions are employed to study the impulsive control system with variable times. The stability criteria on the non-zero solution of the impulsive control system are given by the cone-valued Lyapunov functions and the results of the controllability on the control system are also obtained.
The saddle theorem for multiobjective generalized fractional programming problems with set functions
Sanming Liu,Enmin Feng 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1-2
In this paper, multiobjective generalized fractional programming problems with set functions are considered, in which objective functions are maximum of finite fractional set functions. At first, optimality conditions are established. Then, saddle existence theorem is proved.
Stability and optimal control of microorganisms in continuous culture
Xiaohong Li,Enmin Feng,Zhilong Xiu 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1-2
The process of producing 1,3-preprandiol by microorganism continuous cultivation would attain its equilibrium state. How to get the highest concentration of 1,3-propanediol at that time is the aim for producers. Based on this fact, an optimization model is introduced in this paper, existence of optimal solution is proved. By infinite-dimensional optimal theory, the optimal condition of model is given and the equivalence between optimal condition and the zero of optimality function is proved.