Discretizing continuous-data control systems

A CAD method is presented for converting existing continuous-data control systems into digital control systems by means of a digital controller. The digital controller is synthetized by matching the frequency response of the digital control system to that of the continuous-data system with a minimum weighted mean-square error. A formula for computing the parameters of the digital controller is obtained as a result. The design technique is illustrated with a numerical example and a comparison with previous methods is also presented.     

Optimal control in non-convex domains: a priori discretization error estimates

Abstract An optimal control problem for a two-dimensional elliptic equation with pointwise control constraints is investigated. The domain is assumed to be polygonal but non-convex. The corner singularities are treated by a priori mesh grading. Approximations of the optimal solution of the continuous optimal control problem are constructed by a projection of the discrete adjoint state. It is proved that these approximations have convergence order h². Keywords Linear-quadratic optimal control problems, error estimates, elliptic equations, non-convex domains, corner singularities, control constraints, superconvergence. Mathematics Subject Classification (2000): 49K20, 49M25, 65N30, 65N50     

Digital approximation of continuous-data control systems by point-by-point state comparison

This paper presents a point-by-point state comparison method of approximating a continuous-data system by a sampled-data system. The problem is to attempt the matching of the states of the two systems at the sampling instants. A partial matching has to be conducted if the systems have more states than controls. A weighting matrix is used to regulate the partial matching and weights placed on each state.The digital approximation is affected by use of forward gain E(T) and feedback gain G(T) in the sampled-data system. It is shown that, in general, these gains can be approximated by truncated Taylor series expansions.An illustrative example is given using the one-axis dynamics of the Skylab satellite.     

Distributed parameter system optimum control design via finite element discretization

The problem of designing an optimum distributed parameter system is considered. Fundamental concepts pertaining to the solution of optimum controls for distributed parameter systems by finite element methods are devised. It is demonstrated that methods can readily be applied to solve problems involving nonlinear Neumann boundary conditions.     

Hamiltonian discretization of boundary control systems

A fundamental problem in the simulation and control of complex physical systems containing distributed-parameter components concerns finite-dimensional approximation. Numerical methods for partial differential equations (PDEs) usually assume the boundary conditions to be given, while more often than not the interaction of the distributed-parameter components with the other components takes place precisely via the boundary. On the other hand, finite-dimensional approximation methods for infinite-dimensional input-output systems (e.g., in semi-group format) are not easily relatable to numerical techniques for solving PDEs, and are mainly confined to linear PDEs. In this paper we take a new view on this problem by proposing a method for spatial discretization of boundary control systems based on a particular type of mixed finite elements, resulting in a finite-dimensional input-output system. The approach is based on formulating the distributed-parameter component as an infinite-dimensional port-Hamiltonian system, and exploiting the geometric structure of this representation for the choice of appropriate mixed finite elements. The spatially discretized system is again a port-Hamiltonian system, which can be treated as an approximating lumped-parameter physical system of the same type. In the current paper this program is carried out for the case of an ideal transmission line described by the telegrapher's equations, and for the two-dimensional wave equation.     

变采样网络控制系统的最优保性能控制

研究了一类不确定时延网络控制系统的最优保性能控制问题.针对线性时不变控制对象,控制器和控制对象采用时间-事件驱动,系统成为变采样网络控制系统,考虑在不确定时延小于或者等于一个变采样周期时,基于动态输出反馈对变采样网络控制系统进行建模,利用线性矩阵不等式研究了系统的保性能控制,并设计了保性能控制率和最优保性能控制率,最后给出实例表明在最优保性能控制率的控制下系统稳定.     

Digitalization of continuous-data systems via time-response matching

A computer-aided method to design a digital controller by matching the output response of the digital control system with that of a continuous-data model is proposed in this paper. Golub's algorithm for solving least-squared-errors problems is used to find the coefficients of the optimum digital controller. The advantages of this method are: (1) the order of the digital controller is low, (2) the required sampling frequency is low, (3) the accuracy is high, and (4) the responses in the intersampling periods can be matched. An illustrative example is provided, and a comparison with the results in the available current literature is also made.     

欠驱动冗余度空间机器人优化控制

欠驱动控制是空间技术中容错技术的重要方面.本文研究了被动关节中有制动器的欠驱动冗余度空间机器人系统的运动优化控制问题.从系统动力学方程出发,分析了欠驱动冗余度空间机器人的优化能力和控制方法;给出了主、被动关节间的耦合度指标;提出了欠驱动冗余度空间机器人系统的“虚拟模型引导控制”方法,在这种方法中采用与欠驱动机器人机构等价的全驱动机器人作为模型来规划机器人的运动,使欠驱动系统在关节空间中逼近给出的规划轨迹,实现了机器人末端运动的连续轨迹运动优化控制;通过末关节为被动关节的平面三连杆机器人进行了仿真,仿真的结果证明了提出算法的有效性.     

Optimal control of a Ward Leonard system

Two methods for the optimal control of a Ward Leonard system with quadratic performance index are discussed in this paper. Both the approaches enable the problem to be solved for specified final states and free terminal time. It is seen that the numerical algorithms are straightforward and result in a stable and smooth control trajectory. A numerical example illustrates the close similarity of the results obtained and the improvements in the overall performance that can be expected.     

离散系统最速控制综合函数

针对自抗扰控制技术中的fhan()函数,指出其只是离散系统最速控制综合函数的一种简化.详细推导了离散系统真正的最速控制综合函数——fsun(),完善了自抗扰控制技术的理论框架.理论分析和数值仿真表明,采用fsun()函数后的二阶离散系统,状态变量达到稳态时位置和速度曲线均不会出现超调,且达到稳态时所用的步数少于函数fhan().     

WiMAX系统中的一种最优化准入控制方法

WiMAX正逐渐成为"最后一公里"无线宽带接入的主要解决方案,在WiMAX系统中,准入控制(AC)起着很重要的作用。目前关于AC策略最优化的研究主要考虑服务提供商的利益,即收益最大化,而很少考虑用户的要求。AC策略在收益最大化的基础上增加了关系用户利益的两个约束条件,即阻断率和带宽利用率。实验结果表明,该方法在收益、阻断率、带宽利用率三方面都有良好的性能,兼顾了服务提供商和用户的利益。     

Optimal control of admission to a queueing system

Congestion in a queueing system can sometimes be controlled by restricting arrivals, either by "closing a gate" or by charging an entrance fee or toll. We review both static (open-loop) and dynamic (closed-loop) models for control of admission to a queueing system. The main emphases are on the difference between socially optimal and individually optimal (equilibrium) controls and on the use of dynamic-programming inductive analysis to show that an optimal control is monotonic or characterized by one or more "critical numbers." We discuss the potential for use of these models in the analysis of computer/ communication systems and compare the results to certain others in the literature.     

Open-loop discretization methods for control systems design

In this paper, a unified theory is presented which addresses essential aspects of the open-loop discretization procedure. Initially, factors which affect the generation and propagation of discretization errors are identified by analytical, heuristic and experimental arguments. Following this, a discretization algorithm is presented which takes these factors into account. The fundamental idea of the discretization method is the replacement of the analogue integrators of the prototype continuous-time system by discrete-time approximations. This is done in such a way as to optimize a given cost function with respect to a given input. Unlike many discretization schemes presented in the literature, the procedure developed attempts to first determine the magnitude of the expected discretization errors, and then discretize with an appropriate complexity, giving the designer control over the order of the discrete-time system. This appears to be an effective means of designing filters with low complexity which still retain essential properties of the prototype system. An emphasis of this work is to view the discretization process from a control theory and engineering perspective. This results in a number of new perspectives relating to the discretization process.     

一类排队服务系统的最优控制策略研究

建立一个双阈值排队服务模型, 用来协调顾客的等待时间和服务系统的运行成本. 采用一种精细的概率分解方法获得瞬态和稳态队长的概率分布性质; 再根据系统稳态性能指标, 建立系统营运利润函数, 并设计一种针对双离散变量函数的全局优化收索算法来研究最优控制策略; 进一步的数值实验揭示出双重阈值策略的优越性.     

Optimal discrete-time control system with cost for observation

The problem of how to select the total number and the spacings of the observations optimally when a constant cost is incurred for each observation taken is discussed. Approximate expressions for the criterion function with a fixed number of observations are obtained and are used to determine the optimal total number of observations. For a class of multidimensional systems with a dominant eigenvalue, the problem is shown to reduce to that for scalar systems. Detailed discussion is then carded out for scalar systems including some sensitivity study.     

Optimal control of a water distribution network in a supervisory control system

This paper deals with the use of optimal control techniques in water distribution networks. An optimal control tool, developed in the context of a European research project is described and the application to the city of Sintra (Portugal) is presented.     

资源约束系统的控制与调度协同优化方法

对于一类通信约束的网络控制系统, 应用通信序列的概念和混合逻辑动态的构架, 将其建模成一类集成控制和调度的资源约束系统模型. 采用线性矩阵不等式来描述离散周期系统的周期通信序列和H_∞ 控制的协同优化问题, 并用一种递增优化序列算法来求解优化的调度策略及其相应的渐近稳定及r指数稳定的H_∞控制器. 该算法结合线性矩阵不等式凸优化问题解决了调度与控制的协同设计问题, 同时也节省了搜索优化解的计算时间.     

Planar bipedal locomotion control based on state discretization

In this paper, a new control method for a planar bipedal robot, which we call Graph-based Model Predictive Control, is proposed. This method makes use of a directed graph constructed on the state space of the robot. The vertices of the directed graph are called waypoints, and they serve as intermediate target states to compose complex motions of the robot. By simply tracing the directed edges of the graph, one can achieve Model Predictive Control over the waypoint set. Such a directed graph is pre-designed and stored into the controller’s memory to significantly reduce the computational effort required in real time. In addition, by constructing multiple directed graphs based on different objective functions, one can design multiple motions and switching trajectories among them in a uniform way. The proposed method is applied to variable-speed walking control of a bipedal walker on a two-dimensional plane, and its effectiveness is verified by numerical simulations.