This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncer...This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncertainty in the observation equation of the LQG problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems. The second solution framework considers a general class of discrete-time LQG problems with unknown parameters in both state and observation equations. The best possible (partial) closed-loop feedback control law is derived by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing the optimal nominal dual control.展开更多
In real world situations, most scheduling problems occur neither as complete off-line nor as complete on-line models. Most likely, a problem arises as an on-line model with some partial information. In this article, w...In real world situations, most scheduling problems occur neither as complete off-line nor as complete on-line models. Most likely, a problem arises as an on-line model with some partial information. In this article, we consider such a model. We study the scheduling problem P(n1,n2), where two groups of jobs are to be scheduled. The first job group is available beforehand. As soon as all jobs in the first group are assigned, the second job group appears. The objective is to minimize the longest job completion time (makespan). We show a lower bound of 3/2 even for very special cases. Best possible algorithms are presented for a number of cases. Furthermore, a heuristic is proposed for the general case. The main contribution of this paper is to discuss the impact of the quantity of available information in designing an on-line algorithm. It is interesting to note that the absence of even a little bit information may significantly affect the performance of an algorithm.展开更多
基金the Research Grants Council of Hong Kong, P.R.China under Grant CUHK 4180/03E
文摘This paper summarizes recent progress by the authors in developing two solution frameworks for dual control. The first solution framework considers a class of dual control problems where there exists a parameter uncertainty in the observation equation of the LQG problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems. The second solution framework considers a general class of discrete-time LQG problems with unknown parameters in both state and observation equations. The best possible (partial) closed-loop feedback control law is derived by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing the optimal nominal dual control.
基金Research partially supported by a Hong Kong Government RGC Earmarked Grant.Ref.No.CUHK356/96E Research partially supported by National 973 Fundamental Research Project of china and National Natural Science Foundation of China (19801032)
文摘In real world situations, most scheduling problems occur neither as complete off-line nor as complete on-line models. Most likely, a problem arises as an on-line model with some partial information. In this article, we consider such a model. We study the scheduling problem P(n1,n2), where two groups of jobs are to be scheduled. The first job group is available beforehand. As soon as all jobs in the first group are assigned, the second job group appears. The objective is to minimize the longest job completion time (makespan). We show a lower bound of 3/2 even for very special cases. Best possible algorithms are presented for a number of cases. Furthermore, a heuristic is proposed for the general case. The main contribution of this paper is to discuss the impact of the quantity of available information in designing an on-line algorithm. It is interesting to note that the absence of even a little bit information may significantly affect the performance of an algorithm.
