具有持续扰动的时滞系统前馈2反馈最优控制

针对外部持续扰动下的线性时滞系统，提出一种前馈-反馈最优控制的逐次逼近算法．利用逐次逼近算法，将既含有时滞项又含有超前项的两点边值问题转化为不合时滞项和超前项的线性两点边值问题族，并证明了线性两点边值问题族的解序列一致收敛于原系统最优控制律．得到的最优控制律由解析的无时滞前馈-反馈控制部分和伴随向量序列极限形式的时滞补偿控制部分组成．通过截取时滞补偿序列的有限项，得到系统的前馈-反馈次优控制律．仿真示例表明，该方法对外部持续扰动具有良好的鲁棒性．     

Beam search algorithm for capacity allocation problem in flexible manufacturing systems

This study considers the operation assignment and tool allocation problem in flexible manufacturing systems. A set of operations together with their required tools are selected so as to maximize the total weight. The machines have limited time and tool magazine capacities and the tools are available in limited quantities. We develop a beam search algorithm and obtain near optimal solutions for large size problems very quickly.     

Optimal control of time-varying singular systems using the RK–Butcher algorithm

The problem of optimal control of time-varying linear singular systems with quadratic performance index has been studied using the Runge–Kutta–Butcher algorithm. The results obtained using the Runge–Kutta (RK) method based on the arithmetic mean (RKAM) and the RK–Butcher algorithms are compared with the exact solutions of the time-varying optimal control of linear singular systems. It is observed that the result obtained using the RK–Butcher algorithm is closer to the true solution of the problem. Stability regions for the RKAM algorithm, the single-term Walsh series method and the RK–Butcher algorithms are presented. Error graphs for the simulated results and exact solutions are presented in graphical form to highlight the efficiency of the RK–Butcher algorithm. This algorithm can easily be implemented using a digital computer. An additional advantage of this method is that the solution can be obtained for any length of time for this type of optimal control of time-varying linear singular systems.     

非线性方程组求解的一种新方法

针对现有的非线性方程组求解方法不能同时收敛到所有解的问题,提出了一种混合小生境遗传算法的求解新方法.采用确定性拥挤小生境创造出种群的小生境进化环境,克服遗传算法的遗传漂移现象,维持种群的多样性,使算法能同时收敛到多个解;以拟牛顿算法作为遗传算法的局部搜索算子进行精确搜索,进一步提高算法收敛速度和精度.选择了几组典型的多解非线性方程组进行了求解验证,结果表明所设计的混合小生境遗传算法能在解的定义域内同时收敛到所有解,收敛速度快、精度高,是求解非线性方程组全局解的一种有效方法.     

On communication models for algorithm design in networked sensor systems: A case study

Towards building a systematic methodology of algorithm design for applications of networked sensor systems, we formally define two link-wise communication models, the Collision Free Model (CFM) and the Collision Aware Model (CAM). While CFM provides ease of programming and analysis for high level application functionality, CAM enables more accurate performance analysis and hence more efficient algorithms through cross-layer optimization, at the expense of increased programming and analysis complexity. These communication models are part of an abstract network model, above which algorithm design and performance optimization is performed. We use the example of optimizing a probability based broadcasting scheme under CAM to illustrate algorithm optimization based on the defined models. Specifically, we present an analytical framework that facilitates an accurate modeling and analysis for the probability based broadcasting in CAM (PB_CAM). Our analytical results indicate that (1) the optimal broadcast probability for either maximizing the reachability within a given latency constraint or minimizing the latency for a given reachability constraint decreases rapidly with node density, and (2) the optimal probability for either maximizing the reachability with a given energy constraint or minimizing the energy cost for a given reachability constraint varies slowly between 0 and 0.1 over the entire range of the variations in node density. Our analysis is also confirmed by extensive simulation results.     

A new multi objective optimization approach based on TLBO for location of automatic voltage regulators in distribution systems

This paper proposes a new multi-objective optimization algorithm based on modified teaching–learning-based optimization (MTLBO) algorithm in order to solve the optimal location of automatic voltage regulators (AVRs) in distribution systems at presence of distributed generators (DGs). The objective functions including energy generation costs, electrical energy losses and the voltage deviation are considered in this paper. In the proposed MTLBO algorithm, teacher and learner phases are modified. The considered objective functions are energy generation costs, electrical energy losses and the voltage deviations. The proposed algorithm uses an external repository to save founded Pareto optimal solutions during the search process. Since the objective functions are not the same, a fuzzy clustering method is used to control the size of the repository. The proposed technique allows the decision maker to select one of the Pareto optimal solutions (by compromising) for different applications. The performance of the suggested algorithm on a 70-bus distribution network in comparison with other evolutionary methods such as genetic algorithm (GA), particle swarm optimization (PSO) and TLBO is extraordinary.     

The fixed set search applied to the power dominating set problem

In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.     

A parametric branch and bound approach to suboptimal explicit hybrid MPC

In this article we present a parametric branch and bound algorithm for computation of optimal and suboptimal solutions to parametric mixed-integer quadratic programs and parametric mixed-integer linear programs. The algorithm returns an optimal or suboptimal parametric solution with the level of suboptimality requested by the user. An interesting application of the proposed parametric branch and bound procedure is suboptimal explicit MPC for hybrid systems, where the introduced user-defined suboptimality tolerance reduces the storage requirements and the online computational effort, or even enables the computation of a suboptimal MPC controller in cases where the computation of the optimal MPC controller would be intractable. Moreover, stability of the system in closed loop with the suboptimal controller can be guaranteed a priori.     

An Optimal Control Approach to Linear Systems Controlled by Multiple Controllers

This paper investigates the optimal control design methodology for linear systems which are collaboratively manipulated by multiple agents based on choices such that certain team targets are achieved. By minimizing the average energy cost subject to the set of specified target‐state constraints based on modern variation theory and the Lagrange method, a series of optimal control solutions are established for linear scalar and vector systems jointly controlled by two agents. In addition, a set of sub‐optimal controls are derived, which can lead to a tight upper bound on the average energy cost.     

方块脉冲函数用于求解线性延时系统二次型的最优控制

本文将线性延时系统转化为线性互联非时滞大系统,采用方块脉冲函数不仅得到了最优 控制的分段恒定解答的显式递阶递推公式,而且给出了在线控制的方法.该算法对小延时和 大延时系统均有效,特别易于大延时系统求解.     

一类非线性系统Fokker-Planck方程的解法

通过对一类典型非线性反馈系统的分析,提出一处对一阶和二阶反馈非线性系统的稳态 Fokker-Planck方程的解析解法.根据这一方法,再利用最优降阶技术,提出高阶系统的近似 解,并将其与RDF方法得出的近似解在精度上加以比较,得出有益的结论.     

Modified bang‐bang controller for maximal and minimal time optimal control problems

Recently, there have been a series of results regarding two time optimal control problems for a class of linear and nonlinear systems ‐ one is to keep the system states within certain bound for the longest time during feedback disruption and the other is to derive the system states to near the origin as fast as possible after feedback recovery, both under bounded control inputs. These are called maximal and minimal time optimal control problems, respectively. In the existing results, a bang‐bang controller has been commonly suggested as the actual implementation of the optimal controller. In this paper, we suggest a modified version of the bang‐bang controller which can also serve as an approximate optimal controller. Our proposed controller provides the (near) optimal performance with (i) possible reduction of a number of switchings; (ii) possible reduction of control input magnitude.     

Non-linear singular systems using RK–Butcher algorithms

The Runge–Kutta (RK)–Butcher algorithm is used to study time-invariant and time-varying non-linear singular systems. The results (discrete solutions) obtained using the RK method based on the arithmetic mean (RKAM), single-term Walsh series (STWS) and RK–Butcher algorithms are compared with the exact solutions of the non-linear singular systems for the time-invariant and time-varying cases. It is found that the solution obtained using the RK–Butcher algorithm is closer to the exact solutions of the non-linear singular systems. Stability regions for the RKAM, STWS and RK–Butcher algorithms are presented. Error graphs for discrete and exact solutions are presented in a graphical form to highlight the efficiency of this method. The RK–Butcher algorithm can easily be implemented using a digital computer and the solution can be obtained for any length of time for both time-invariant and time-varying cases for these non-linear singular systems, which is an added advantage of this algorithm.     

分布估计算法在航天器近距离最优交会中的应用

针对空间在轨服务飞行器实施近距离变轨最优化问题,探讨了在能量和时间两项指标情况下,航天器轨道机动中能量时间综合最优化的研究方法。基于C-W方程,推导了在轨服务器在双冲量变轨时的特征速度,以时间-燃料为指标构造了相应的模型,并针对基本遗传算法局部搜索能力不强的问题,采用一种新的利用统计学习手段从群体宏观角度建立描述解分布的分布估计算法。仿真结果表明,该分布估计算法可加速算法的收敛,具有良好的优化能力,能够从宏观上对整个群体建立模型,得到了混合指标下时间和能量关系,实现近距离变轨最优指标的精确数值模拟。从数值结果的对比分析中得出了一些有意义的结论,可供下一步研究参考。     

Chaotic Sandpiper Optimization Based Virtual Machine Scheduling for Cyber-Physical Systems

Recently, with the growth of cyber physical systems (CPS), several applications have begun to deploy in the CPS for connecting the cyber space with the physical scale effectively. Besides, the cloud computing (CC) enabled CPS offers huge processing and storage resources for CPS that finds helpful for a range of application areas. At the same time, with the massive development of applications that exist in the CPS environment, the energy utilization of the cloud enabled CPS has gained significant interest. For improving the energy effectiveness of the CC platform, virtualization technologies have been employed for resource management and the applications are executed via virtual machines (VMs). Since effective scheduling of resources acts as an important role in the design of cloud enabled CPS, this paper focuses on the design of chaotic sandpiper optimization based VM scheduling (CSPO-VMS) technique for energy efficient CPS. The CSPO-VMS technique is utilized for searching for the optimum VM migration solution and it helps to choose an effective scheduling strategy. The CSPO algorithm integrates the concepts of traditional SPO algorithm with the chaos theory, which substitutes the main parameter and combines it with the chaos. In order to improve the process of determining the global optimum solutions and convergence rate of the SPO algorithm, the chaotic concept is included in the SPO algorithm. The CSPO-VMS technique also derives a fitness function to choose optimal scheduling strategy in the CPS environment. In order to demonstrate the enhanced performance of the CSPO-VMS technique, a wide range of simulations were carried out and the results are examined under varying aspects. The simulation results ensured the improved performance of the CSPO-VMS technique over the recent methods interms of different measures.     

An evolutionary algorithm for optimizing material flow in supply chains

Supply chain management literature calls for coordination between the different members of the chain. Materials should be moved from one supplier to the next according to a just-in-time schedule. In this paper we develop an evolutionary algorithm (EA) for optimal synchronization of supply chains. In developing our algorithm, we use the economic delivery and scheduling model and analyze supply chains dealing with multiple-components. We test the performance of the proposed EA and show that it provides optimal, or near optimal, solutions for a wide range of problems. The EA is shown to be much faster at solving large problems than an enumeration procedure and exhibits robust behavior when tested on a variety of different problem parameters.     

A constrained minimum variance input-output estimator for linear dynamic systems

A stationary estimator is presented that provides estimates for both the outputs and the inputs of linear time-invariant systems. The estimates satisfy the input-output equations and are optimal in a weighted minimum variance sense. It is shown that the true optimum problem is too complicated to allow a general closed-form solution and a sub-optimal approach is suggested that leads to a simple computational algorithm.     

开销敏感的多处理器最优节能实时调度算法

嵌入式多处理器系统的能耗问题变得日益重要,如何减少能耗同时满足实时约束成为多处理器系统节能实时调度中的一个重要问题.目前绝大多数研究基于关键速度降低处理器的频率以减少动态能耗,采用关闭处理器的方法减少静态能耗.虽然这种方法可以实现节能,但是不能保证最小化能耗.而现有最优的节能实时调度未考虑处理器状态切换的时间和能量开销,因此在切换开销不可忽视的实际平台中不再是最优的.文中针对具有独立动态电压频率调节和动态功耗管理功能的多处理器系统,考虑处理器切换开销,提出一种基于帧任务模型的最优节能实时调度算法.该算法根据关键速度来判断系统负载情况,确定具有最低能耗值的活跃处理器个数,然后根据状态切换开销来确定最优调度序列.该算法允许实时任务在处理器之间任意迁移,计算复杂度小,易于实现.数学分析证明了该算法的最优性.     

An algorithm for optimal decentralized regulation of linear quadratic interconnected systems

This paper provides a method for designing ‘optimal’ decentralized controls for linear time-invariant interconnected systems. The optimality is with respect to a quadratic cost criterion. An algorithm is proposed which uses the method of feasible directions and provides a local minimum while ensuring, at each iteration, the stability of the overall system.