Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle

A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived from a given system by using the stochastic averaging method for quasi-Hamiltonian systems with uncertain parameters. Then, the stochastic Hamiltonian system for minimax optimal control with a given performance index is established based on the stochastic maximum principle. The worst disturbances are determined by minimizing the Hamiltonian function, and the worst-case optimal controls are obtained by maximizing the minimal Hamiltonian function. The differential equation for adjoint process as a function of system energy is derived from the adjoint equation by using the Itô differential rule. Finally, two examples of controlled uncertain quasi-Hamiltonian systems are worked out to illustrate the application and effectiveness of the proposed control strategy.     

一类不确定系统的最优极小极大鲁棒控制

讨论一类不确定系统的极小极大鲁棒动态输出反馈控制问题.给出不确定系统的极小极大鲁棒控制的定义.利用线性矩阵不等式(LMI)处理方法和Lyapunov稳定性理论,得到了在干扰和不确定性最大的情形下极小极大输出反馈控制器存在的充分条件.引入凸优化技术, 求得最优极小极大控制器.它不仅保证闭环系统渐近稳定, 且使得闭环系统性能指标的上界最小.仿真算例说明了所设计的控制器具有较强的干扰抑制功能.     

云工作流系统中能耗感知的任务调度算法*

云工作流系统研究集中在工作流任务执行的时间效率优化,然而时间最优的任务调度方案可能存在不同能耗,因此,文中求解满足时间约束时能耗最优的调度方案。首先改进任务执行能耗模型,设计适用于评价任务调度方案执行能耗的适应度计算方法。然后基于精准调整粒子速度的自适应权重,提出解决任务调度能耗优化问题的自适应粒子群算法。实验表明,文中算法收敛稳定,调度方案执行能耗较低。     

智能控制在地铁通风空调系统中的应用

通风空调系统作为地铁中的重要设备系统之一,担负着对地下空间的空气温度、湿度、空气流速和空气品质进行控制的任务,而其能耗约为地下线能耗的30%以上,仅次于车辆牵引用电能耗,节能潜力相对较大。介绍了通风空调系统的运行模式和能耗测量方法,在分析能耗数据及能耗的基础上,提出了空调系统智能控制模块在环境综合监控系统(BAS)中的实现方案。     

Mini-max method for optimization of energy consumption in real-time systems with a lot of processing elements

The mini-max method is designed for the analysis and optimization of energy consumption in single-processor real-time systems and offers several advantages over alternative methods when used in single-task and multitask systems. There has been no research, however, dedicated to its use in real-time systems with several processing elements. This work deals with the use of the mini-max method in subsystems with two executive elements. Two methods for the organization of systems processing sequential task threads are proposed. The first method is a synchronous one with an allotted time period for each task, and the second method involves an asynchronous task stream. The analysis and comparison of these methods are performed, and their efficiency in solving the problem of energy consumption is shown.     

Image thresholding by variational minimax optimization

In this paper we introduce an adaptive image thresholding technique via minimax optimization of a novel energy functional that consists of a non-linear convex combination of an edge sensitive data fidelity term and a regularization term. While the proposed data fidelity term requires the threshold surface to intersect the image surface only at places with large image gradient magnitude, the regularization term enforces smoothness in the threshold surface. To the best of our knowledge, all the previously proposed energy functional-based adaptive image thresholding algorithms rely on manually set weighting parameters to achieve a balance between the data fidelity and the regularization terms. In contrast, we use minimax principle to automatically find this weighting parameter value, as well as the threshold surface. Our conscious choice of the energy functional permits a variational formulation within the minimax principle leading to a globally optimum solution. The proposed variational minimax optimization is carried out by an iterative gradient descent with exact line search technique that we experimentally demonstrate to be computationally far more attractive than the Fibonacci search applied to find the minimax solution. Our method shows promising results to preserve edge/texture structures in different benchmark images over other competing methods. We also demonstrate the efficacy of the proposed method for delineating lung boundaries from magnetic resonance imagery (MRI).     

Design of input shapers using modal cost for multi-mode systems

This paper presents two techniques for the determination of modal weights for the design of robust input shapers for multi-mode systems. The weights for the first technique are derived based on the scaling factor for the potential energy in each mode, such that the modal displacement is the same. The second technique exploits the modal cost analysis which uses the angle between the right eigenvectors and the row vectors of the output matrix to determine the contribution of each mode to the output. Two examples are used to illustrate the improvement in performance of the modal weighted minimax shapers compared to the traditional minimax shaper which equally weights all the modes.     

不确定拟哈密顿系统的随机最优控制

本文提出了不确定拟哈密顿系统、基于随机平均法、随机极大值原理和随机微分对策理论的一种随机极大极小最优控制策略.首先,运用拟哈密顿系统的随机平均法,将系统状态从速度和位移的快变量形式转化为能量的慢变量形式,得到部分平均的It随机微分方程;其次,给定控制性能指标,对于不确定拟哈密顿系统的随机最优控制,根据随机微分对策理论,将其转化为一个极小极大控制问题;再根据随机极大值原理,建立关于系统与伴随过程的前向-后向随机微分方程,随机最优控制表达为哈密顿控制函数的极大极小条件,由此得到最坏情形下的扰动参数与极大极小最优控制;然后,将最坏扰动参数与最优控制代入部分平均的It随机微分方程并完成平均,求解与完全平均的It随机微分方程相应的Fokker-Planck-Kolmogorov(FPK)方程,可得受控系统的响应量并计算控制效果;最后,将上述不确定拟哈密顿系统的随机最优控制策略应用于一个两自由度非线性系统,通过数值结果说明该随机极大极小控制策略的控制效果.     

Optimizing a combined WCET-WCEC problem in instruction fetching for real-time systems

In real-time systems, time is usually so critical that other parameters such as energy consumption are often not even considered. However, optimizing the worst energy consumption case can be a key factor in systems with severe power-supply limitations. In this paper we study several memory architectures using combined time and energy optimization models for real-time multitasking systems. Each task is modeled using Lock-MS, a method to optimize the WCET of a task, with an added set of constraints to model in the same way the WCEC (worst case energy consumption). Our tested hardware components focus on instruction fetching, including a lockable cache, a line buffer and a sequential prefetch buffer. We test a variety of instruction fetch alternatives optimizing time and energy consumption. Our results show that the accuracy of the estimation of the number of context switches in the worst case may affect very much the resulting WCEC (up to 8 times in our experiments) and that optimizing the WCEC may provide similar execution times than optimizing the WCET, with up to 5 times less energy consumption Additionally optimization functions combining WCET and WCEC with different weights show very interesting WCET-WCEC trade-offs. This confirms that methodologies testing such optimizations at design time could be very helpful to provide a precise system set-up.     

E-mc2: A formal framework for energy modelling in cloud computing

Due to energy crisis of the last years, energy waste and sustainability have been brought both into public attention, and under industry and scientific scrutiny. Thus, obtaining high-performance at a reduced cost in cloud environments as reached a turning point where computing power is no longer the most important concern. However, the emphasis is shifting to manage energy efficiently, whereas providing techniques for measuring energy requirements in cloud systems becomes of capital importance.Currently there are different methods for measuring energy consumption in computer systems. The first consists in using power meter devices, which measure the aggregated power use of a machine. Another method involves directly instrumenting the motherboard with multimeters in order to obtain each power connector’s voltage and current, thus obtaining real-time power consumption. These techniques provide a very accurate results, but they are not suitable for large-scale environments. On the contrary, simulation techniques provide good scalability for performing experiments of energy consumption in cloud environments. In this paper we propose E-mc², a formal framework integrated into the iCanCloud simulation platform for modelling the energy requirements in cloud computing systems.     

基于粒子群算法的非线性方程组求解

将非线性方程组的求解问题转化为无约束极大极小优化问题,并应用一种新的进化计算（EC）方法——粒子群算法（PSO）求解此优化问题。数值实验的结果验证了该方法的可行性和有效性。     

Sleep-aware mode assignment in wireless embedded systems

Minimizing energy consumption is a key issue in designing wireless embedded systems. While a lot of work has been done to manage energy consumption on single processor real-time systems, little work has been done in network-wide energy consumption management for real-time tasks. Existing work on network-wide energy minimization assumes that the underlying network is always connected, which is not consistent with the practice in which wireless nodes often turn off their network interfaces in a sleep schedule to reduce energy consumption. Moreover, existing sleep scheduling techniques are unaware of computation status and often lead to unnecessary wakeup overheads. In this paper, we propose solutions to minimize network-wide energy consumption for real-time tasks with precedence constraints executing on wireless embedded systems. Our solutions jointly consider the radio sleep scheduling of wireless nodes and the execution modes of processors. Based on different wireless network topologies, we propose energy management schemes to minimize energy consumption while guaranteeing the timing constraint and precedence constraint. When the precedence graph is a tree, our solution gives optimal result on energy management. The experiments show that our approach significantly reduces total energy consumption compared with previous works.     

Stochastic nonlinear minimax dynamic games with noisy measurements

This note is concerned with nonlinear stochastic minimax dynamic games which are subject to noisy measurements. The minimizing players are control inputs while the maximizing players are square-integrable stochastic processes. The minimax dynamic game is formulated using an information state, which depends on the paths of the observed processes. The information state satisfies a partial differential equation of the Hamilton-Jacobi-Bellman (HJB) type. The HJB equation is employed to characterize the dissipation properties of the system, to derive a separation theorem between the design of the estimator and the controller, and to introduce a certainty-equivalence principle along the lines of Whittle. Finally, the separation theorem and the certainty-equi. valence principle are applied to solve the linear-quadratic-Gaussian minimax game. The results of this note generalize the L/sup 2/-gain of deterministic systems to stochastic analogs; they are related to the controller design of stochastic systems which employ risk-sensitive performance criteria, and to the controller design of deterministic systems which employ minimax performance criteria.     

A New Approach for Numerically Solving Nonlinear Eigensolution Problems

By considering a constraint on the energy profile, a new implicit approach is developed to solve nonlinear eigensolution problems. A corresponding minimax method is modified to numerically find eigensolutions in the order of their eigenvalues to a class of semilinear elliptic eigensolution problems from nonlinear optics and other nonlinear dispersive/diffusion systems. It turns out that the constraint is equivalent to a constraint on the wave intensity in L-(p+1) norm. The new approach enables people to establish some interesting new properties, such as wave intensity preserving/control, bifurcation identification, etc., and to explore their applications. Numerical results are presented to illustrate the method.     

Minimax control for discrete-time time-varying stochastic systems

This paper gives a self-contained presentation of minimax control for discrete-time time-varying stochastic systems under finite- and infinite-horizon expected total cost performance criteria. Suitable conditions for the existence of minimax strategies are proposed. Also, we prove that the values of the finite-horizon problem converge to the values of the infinite-horizon problems. Moreover, for finite-horizon problems an algorithm of calculation of minimax strategies is developed and tested by using time-varying stochastic systems.     

Robust tracking enhancement of robot systems including motordynamics: a fuzzy-based dynamic game approach

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance     

一类广义时滞系统的极小极大控制

研究一类广义时滞系统的极小极大控制问题,目的是利用构造局部检验函数的方法设计极小极大控制器,使得在最坏的干扰下系统的性能指标上界极小.利用线性矩阵不等式(LM I)给出了广义时滞系统极小极大控制器存在的充分条件,讨论了闭环系统的容许性,并将所得结果推广到含有不确定性的广义时滞系统.最后以数值算例说明了所提出的控制器设计方法的有效性和可行性.     

An energy-saving optimization method for cyclic pick-and-place tasks based on flexible joint configurations

Optimizing the energy consumption of robot movements becomes one of the increasingly important issues in industry. Minimizing a robot's movement has been identified as one of the strategies to improve energy efficiency in robotic systems. In this paper, a mathematical model of the total energy consumption of cycle pick-and-place tasks is proposed, which considers operating motion and homing motion of a given trajectory with different joint configurations. Optimal joint configurations for cyclic pick-and-place tasks are investigated in order to maximize energy saving. Finally, a case study is described to illustrate the proposed method and the results show that compared with fixed joint configurations, the proposed method based on flexible joint configurations reduces the energy consumption by 10.33%.     

Robust state estimation in uncertain systems: Combined detection-estimation with incremental MSE criterion

Minimax state estimation for uncertain systems is discussed. The conservative performance of the standard minimax estimator in the absence of an intelligent adversary is reduced by a combined detectorestimator structure and an incremental mean-squared error (IMSE) performance criterion. The optimal structure is defined for a wide class of linear and nonlinear systems whose uncertain parameters are elements of some known compact space and is also obtained for convex parameter spaces. Since the complete specification of the optimal estimator detector is problem dependent, a computational procedure is outlined. In an example, the resulting combined detector-estimator is shown to increase the estimation accuracy in the incremental minimax sense by a factor of two over the standard minimax estimator.     

基于T-S模型的非线性系统非脆弱极小极大控制

研究一类非线性离散系统的鲁棒非脆弱极小极大控制问题.针对含有不确定项的非线性离散系统,构造T-S模型,引入参数不确定项,使得模糊模型能够更精确逼近原系统.考虑系统和控制器同时含有不确定性,利用线性矩阵不等式(LMI)处理方法和Lyapunov稳定性理论,设计鲁棒且非脆弱的控制器.考虑不确定性使得性能指标最大的情形,得到极小极大鲁棒非脆弱控制器存在的充分条件.引入凸优化算法,求解使闭环系统渐近稳定且性能指标上界最小的最优极小极大鲁棒控制器的参数.最后以著名的truck-trailer模型为例的仿真结果表明所设计的控制器具有良好的鲁棒性和非脆弱性.