椭圆参考轨道指定区域最优交会研究

研究了椭圆参考轨道指定区域最优交会问题。为了实现在指定区域完成最优交会,采用以参考轨道真近点角为自变量的线性化时变Tschauner-Hempel交会动力学模型,按照设定的真近点角交会域和最优二次性能指标设计最优交会控制,加权矩阵随真近点角变化。为方便指定区域最优控制问题求解,采用区段混合能法递推求解时变黎卡提矩阵微分方程和状态轨线。对远距、近距异面交会和共面交会三种情况设定不同的交会域进行了仿真研究,结果表明方法能保证在设定的真近点角域内完成交会,交会控制能耗小,精度高。     

基于最优模糊PID温度控制方法研究

针对某智能大厦空调的温度控制系统,引入了一种新的模糊推理方法,设计了模糊PID控制器.该模糊推理方法将优化和反馈的思想引入推理过程中,依据不同的优化指标进行推理,使推理过程更为有效,论文给出了应用该推理方法的具体过程.以建立起的温度系统模型为基础,设计了基于最优模糊推理的温度系统模糊PID控制器,进行了仿真研究,仿真结果和实际运行表明了该控制方法具有强鲁棒性和良好控制品质.     

Trading a mean-reverting asset: Buy low and sell high

This paper is concerned with an optimal trading (buy and sell) rule. The underlying asset price is governed by a mean-reverting model. The objective is to buy and sell the asset so as to maximize the overall return. Slippage cost is imposed on each transaction. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the original optimal stopping problem can be obtained by solving two quasi-algebraic equations. Sufficient conditions are given in the form of a verification theorem. A numerical example is reported to demonstrate the results.     

Solving the Beck and Wieland model with optimal experimentation in DualPC

Currently, there is a renewed interest in the use of optimal experimentation (adaptive control) in economics. Example are found in [Amman and Kendrick, 1999], [Amman and Kendrick, 2003], [Cosimano, in?press], [Cosimano and Gapen, 2005b], [Cosimano and Gapen, 2005a], [Cosimano and Gapen, 2006], [Tesfaselassie et?al., 2007], [Tucci, 1997], [Wieland, 2000a] and [Wieland, 2000b]. In this paper we present the Beck & Wieland model [Beck, G., & Wieland, V. (2002). Learning and control in a changing economic environment. Journal of Economic Dynamics and Control, 26, 1359-1378] and the methodology to solve this model with time-varying parameters using the various control methods described in [Kendrick, 1981] and [Kendrick, 2002]. Furthermore, we also provide numerical results using the DualPC software [Amman, H. M., & Kendrick, D. A. (1999). The DualI/DualPC software for optimal control models: User’s guide. Working paper, Austin, TX 78712, USA: Center for Applied Research in Economics, University of Texas] and show first evidence that optimal experimentation or Dual Control may produce better results than Expected Optimal Feedback.     

二级倒立摆的建模与MATLAB仿真

通过对二级倒立摆结构构成及平衡控制问题的分析,给出基于牛顿力学定律的数学建模方法,并应用二次型最优控制理论实现二级倒立摆控制。根据MATLAB仿真结果表明,建模方法可行,采用二次型最优控制对系统进行控制,能满足控制系统稳定性、鲁棒性要求。     

关键词最优路径查询的分段拓展算法

关键词最优路径查询（KOR）查找在满足关键词全覆盖和路径长度约束条件下,时间开销最小的路线常用于旅行规划。现有优化算法虽然采用各种剪枝策略缩小搜索规模,但是本质上是广度优先搜索,在查找长路径时,搜索规模依然过大,执行时间长。针对该问题,提出一种关键词最优路径查询的分段拓展算法（SE-KOR）。SE-KOR算法根据关键词倒排索引表构建关键词顶点路径,将路径划分为多段分别拓展,降低搜索规模,从而缩短执行时间。该算法在路径拓展时给出路径走向,而现有剪枝策略不控制路径拓展方向,因此提出局部代价阈值剪枝,控制路径的走向沿关键词顶点路径拓展,并综合运用近似支配、可行解目标值剪枝和全局优先拓展策略加速拓展。实验结果表明,在不损失精度的情况下,该算法执行时间分别在不同关键词个数、代价阈值与查询图规模下至少缩短8.0%、61.0%和57.7%。     

The optimal control approach to generalized multiprocessor scheduling

In this paper we present several new results in the theory of homogeneous multiprocessor scheduling. We start with some assumptions about the behavior of tasks, with associated precedence constraints, as processor power is applied. We assume that as more processors are applied to a task, the time taken to compute it decreases, yielding some speedup. Because of communication, synchronization, and task scheduling overhead, this speedup increases less than linearly with the number of processors applied. We also assume that the number of processors which can be assigned to a task is a continuous variable, with a view to exploiting continuous mathematics. The optimal scheduling problem is to determine the number of processors assigned to each task, and task sequencing, to minimize the finishing time.These assumptions allow us to recast the optimal scheduling problem in a form which can be addressed by optimal control theory. Various theorems can be proven which characterize the optimal scheduling solution. Most importantly, for the special case where the speedup function of each task isp , wherep is the amount of processing power applied to the task, we can directly solve our equations for the optimal solution. In this case, for task graphs formed from parallel and series connections, the solution can be derived by inspection. The solution can also be shown to be shortest path from the initial to the final state, as measured by anl _1/ distance metric, subject to obstacle constraints imposed by the precedence constraints.This research has been funded in part by the Advanced Research Project Agency monitored by ONR under Grant No. N00014-89-J-1489, in part by Draper Laboratory, in part by DARPA Contract No. N00014-87-K-0825, and in part by NSF Grant No. MIP-9012773. The first author is now with AT&T Bell Laboratories and the second author is with BBN Incorporated.     

Approximate dynamic programming solutions with a single network adaptive critic for a class of nonlinear systems

Approximate dynamic programming (ADP) formulation implemented with an adaptive critic (AC)-based neural network (NN) structure has evolved as a powerful technique for solving the Hamilton-Jacobi-Bellman (HJB) equations. As interest in ADP and the AC solutions are escalating with time, there is a dire need to consider possible enabling factors for their implementations. A typical AC structure consists of two interacting NNs, which is computationally expensive. In this paper, a new architecture, called the ‘cost-function-based single network adaptive critic (J-SNAC)’ is presented, which eliminates one of the networks in a typical AC structure. This approach is applicable to a wide class of nonlinear systems in engineering. In order to demonstrate the benefits and the control synthesis with the J-SNAC, two problems have been solved with the AC and the J-SNAC approaches. Results are presented, which show savings of about 50% of the computational costs by J-SNAC while having the same accuracy levels of the dual network structure in solving for optimal control. Furthermore, convergence of the J-SNAC iterations, which reduces to a least-squares problem, is discussed; for linear systems, the iterative process is shown to reduce to solving the familiar algebraic Ricatti equation.     

A review of stochastic algorithms with continuous value function approximation and some new approximate policy iteration algorithms for multidimensional continuous applications

We review the literature on approximate dynamic programming, with the goal of better understanding the theory behind practical algorithms for solving dynamic programs with continuous and vector-valued states and actions and complex information processes. We build on the literature that has addressed the well-known problem of multidimensional (and possibly continuous) states, and the extensive literature on model-free dynamic programming, which also assumes that the expectation in Bellman’s equation cannot be computed. However, we point out complications that arise when the actions/controls are vector-valued and possibly continuous. We then describe some recent research by the authors on approximate policy iteration algorithms that offer convergence guarantees (with technical assumptions) for both parametric and nonparametric architectures for the value function.