在逐点状态约束下一个四阶线性系统的时间最优控制

在逐点状态约束下,最优控制问题的求解是很困难的,已有的最大值原理和形态规划理论很难用来求解在逐点状态约束下最优控制问题.本文讨论逐点状态约束下一个四阶线性系统的时间最优控制问题.我们采用转换的方法给出了最优时间与最优控制的具体表达式.     

Time/fuel optimal control of constrained linear discrete systems

A unified approach to solving three common optimal control problems is presented, for linear systems under general constraints. The problems are: (1) the time optimal control problem; (2) the fuel optimal control problem in fixed time; (3) the time optimal control problem with a fuel constraint. A special purpose linear programming algorithm is used. State variable constraints are efficiently handled by a cutting plane algorithm. An example of a sixth order system with two inputs and two state variable constraints illustrates the method as implemented on a personal computer.     

面向微粒操纵的介电泳芯片系统研究

针对目前在纳米器件及传感器的制造中尚无对大量粒子进行有效操纵的方法,我们利用介电泳方法对大量微粒进行定位和传输操纵,介绍了利用MEMS工艺进行介电泳芯片加工的过程以及整个观测与实验系统的建立,通过有限元软件对传统介电泳和行波介电泳中电极阵列的电场分布进行求解,并在该实验系统下实现了对微通道中的悬浮高度和微粒的运动速度的测量.该实验系统的研究为液体环境下微纳颗粒的装配和分离提供了一条有效的技术路径.     

Properties of optimal stochastic control systems with dead-time

Structural, stability and sensitivity properties of optimal stochastic control systems for dead-time, stable minimum phase as well as non-minimum phase processes are presented. The processes are described by rational transfer functions plus dead-times and the disturbances by rational spectral densities. It is shown that although the frequency domain design techniques guarantee asymptotically stable systems for given process and disturbance models, many of the designs might be practically unstable. Necessary and sufficient conditions that must be imposed on the design to assure practically stable optimal systems are derived. The uncertainties in the parameters and in the structure of the process model are measured by means of an ignorance function. Sufficient conditions in terms of the ignorance function, which guarantee stable design and by means of which the bounds of the uncertainties for a given design may be estimated, are stated. Conditions under which the optimal designs possess attractive relative stability properties, namely gain and phase margins of at least 2 and 60°, respectively, are stated, too. It is further shown that any optimal controller, for the type of processes discussed in this paper, may be separated into a primary controller and into a dead-time compensator where the latter is completely independent of the cost and the disturbance properties. Such a decomposition gives excellent insight into the role of the cost and the disturbance in the design. When low order process and disturbance models are used, the conventional PI and PID control laws coupled with the dead-time compensator emerge.     

Rate limited time optimal control of a planar pendulum

Time optimal control problems often admit as solution bang-bang controls but they present several drawbacks in real applications where additional degrees of regularity are desirable. In this paper, the rate limited time optimal swing up of an inverted pendulum is considered and necessary conditions that have to be satisfied by optimal trajectories in the presence of rate constraints are derived. A comparison between this approach and the results from the standard time optimal problem is reported.     

移动机器人速度加速度饱和约束下的时间最优控制

针对机器人运动系统中普遍存在的速度和加速度约束, 提出一种满足以上约束的机器人运动时间最优控制方法. 首先, 通过最优条件构造哈密尔顿函数, 根据极小值原理求解时间最优控制; 其次, 通过相轨迹分析, 证明了满足约束的时间最优控制律的形式; 再次, 通过求解最优时间, 将满足约束的时间最优控制律转换成末端时间为最优时间的燃料最优控制律; 最后, 在RoboCup 小型足球机器人上进行对比实验, 验证了该方法在规划与实际上的一致性.     

基于LQR的直升机最优控制系统的设计

设计了直升机LQR最优控制系统，并针对LQR控制中加权矩阵和难以确定的问题，进行了试验分析，从实际控制效果出发．找出了系统响应与和之间遵循的规律，为在利用该方法进行其它控制系统设计中和的选取提供了参考。     

求解量子系统时间最优控制问题的同伦算法研究

针对数值求解量子系统时间最优控制问题中反复调用梯度算法导致计算量大的问题,本文提出一类同伦算法用以快速求解量子系统的时间最优控制问题.与已有算法不同,这一算法通过引入同伦变量在减小终端时间的方向上搜索最优解.在这一算法中,可通过自由函数构造保真度函数对控制变量的梯度方向,也可通过方向函数引导算法的搜索方向,以加快算法的搜索速度.本文将这一算法用于求解量子系统态转移和门变换的时间最优控制问题.仿真结果表明这一算法的有效性.     

The existence of time optimal control of semilinear parabolic equations

This work is concerned with the existence of the time optimal control for some semilinear parabolic differential equations with control distributed in a subdomain.     

Continuous dependence of optimal control to controlled domain of actuator for heat equation

In this paper, we consider continuous dependence of the optimal control with respect to the actuator domain which is varying as open subset in the spatial domain for a multi-dimensional heat equation. Both time optimal control and norm optimal control problems are considered. The reason behind combining these two problems together is that these two problems are actually equivalent: The energy to be used to drive the system to target set in minimal time interval is actually the minimal energy of driving the system to target set in this minimal time interval, and visa versa. It is shown that both optimal control and optimal cost are continuous with respect to open controlled actuator domain under the Lebesgue measure.     

On the practical stability of optimal stochastic control systems with dead-time

The practical stability of optimal stochastic control systems for processes having dead-times is considered. Previously obtained necessary conditions for practical stability of such systems are generalized using Pontryagin's theorem on the roots of two-variable polynomials. The conditions are expressed in terms of the relations between the orders of the process, the process model and the disturbance model.     

Multivariable norm optimal and parameter optimal iterative learning control: a unified formulation

This article investigates the two paradigms of norm optimal iterative learning control (NOILC) and parameter optimal iterative learning control (POILC) for multivariable (MIMO) ?-input, m-output linear discrete-time systems. The main result is a proof that, despite their algebraic and conceptual differences, they can be unified using linear quadratic multi-parameter optimisation techniques. In particular, whilst POILC has been naturally regarded as an approximation to NOILC, it is shown that the NOILC control law can be generated from a suitable choice of control law parameterisation and objective function in a multi-parameter MIMO POILC problem. The form of this equivalence is used to propose a new general approach to the construction of POILC problems for MIMO systems that approximates the solution of a given NOILC problem. An infinite number of such approximations exist. This great diversity is illustrated by the derivation of new convergent algorithms based on time interval and gradient partition that extend previously published work.     

Bilinear optimal control of a Kirchhoff plate

We consider the problem of optimal control of a Kirchhoff plate. A bilinear control is used as a force to make the plate close to a desired profile taking into the account, a quadratic cost of control. We prove the existence of an optimal control and characterize it uniquely through the solution of an optimality system.     

Computation of feedback control for time optimal state transfer using Groebner basis

Computation of time optimal feedback control law for a controllable linear time invariant system with bounded inputs is considered. Unlike a recent paper by the authors, the target final state is not limited to the origin of state-space, but is allowed to be in the set of constrained controllable states. Switching surfaces are formulated as semi-algebraic sets using Groebner basis based elimination theory. Using these semi-algebraic sets, a nested switching logic is synthesized to generate the time optimal feedback control. However, the optimal control law enforces an unavoidable limit cycle in the time-optimal trajectory for most non-origin target points. The time-period of this limit-cycle is dependent on the target position. This dependence is algebraically characterized and a method to compute the time-period of the limit-cycle is provided. As a natural extension, the set of constrained controllable states is also computed.     

多回路网络化控制系统中优化采样频率的确定

在多回路网络化控制系统中，通讯资源的共享和网络传输的时延为系统分析和设计带来新的问题．运用非线性规划理论，分析和推导了多回路网络化控制系统中采样频率优化问题，并由推导过程归纳出易于计算机编程实现的工程化求解方法．通过仿真示例验证了所提出方法的有效性．     

Intelligent optimal control system for ball mill grinding process

Operation aim of ball mill grinding process is to control grinding particle size and circulation load to ball mill into their objective limits respectively, while guaranteeing producing safely and stably. The grinding process is essentially a multi-input multi-output system (MIMO) with large inertia, strong coupling and uncertainty characteristics. Furthermore, being unable to monitor the particle size online in most of concentrator plants, it is difficult to realize the optimal control by adopting traditional control methods based on mathematical models. In this paper, an intelligent optimal control method with two-layer hierarchical construction is presented. Based on fuzzy and rule-based reasoning (RBR) algorithms, the intelligent optimal setting layer generates the loops setpoints of the basic control layer, and the latter can track their setpoints with decentralized PID algorithms. With the distributed control system (DCS) platform, the proposed control method has been built and implemented in a concentration plant in Gansu province, China. The industrial application indicates the validation and effectiveness of the proposed method.     

An optimal control for a flotation circuit

The optimal operation of a flotation circuit, which is used to separate two minerals is discussed. The optimal control of the flotation circuit at Lake Dufault is found to be a bang-bang control, to contain a singular sub-arc, or to be totally singular depending on the various practical constraints. The influence of the time-delay on the optimal control of the flotation circuit is then investigated. Although the influence of the delay is quite significant, the basic structure of the optimal policy remains roughly the same. Thus it is not unreasonable to ignore the delay, although the optimality suffers from this.     

The problem of LQG optimal control via a limited capacity communication channel

The paper addresses a LQG optimal control problem involving bit-rate communication capacity constraints. A discrete-time partially observed system perturbed by white noises is studied. Unlike the classic LQG control theory, the control signal must be first encoded, then transmitted to the actuators over a digital communication channel with a given bandwidth, and finally decoded. Both the control law and the algorithms of encoding and decoding should be designed to archive the best performance. The optimal control strategy is obtained. It is shown that where the estimator-coder separation principle holds, the controller-coder one fails to be true.     

非周期软实时系统的动态最优控制方法

运用多优先级排队系统的分析方法,研究了到达时刻和执行时间均不确定的非周期软实时系统,提出了一种针对DM调度算法的动态最优控制方法。该方法能在统计意义上确保系统的实时性,同时又兼顾系统的QoS需求和提高系统吞吐率。实例表明,该方法能提高系统的实际利用率,降低系统的截止时间错过率,是一种有效的载荷管理方法。