基于神经动态优化的非线性系统近似最优跟踪控制

提出一种输入约束下一类连续时间非线性系统最优跟踪控制问题的近似求解方法.针对有限时间跟踪性能指标下一类单输入单输出非线性系统,利用所提出的最优跟踪控制方法实现目标系统所对应性能指标近似最优.首先将系统的性能指标沿时间泰勒展开,得到一个近似的性能指标;其次,在系统状态可观测条件下,将该问题进一步转化为以控制输入为决策变量的非线性规划问题;再次,利用神经动态优化方法,求解含不等式约束下的近似最优控制问题并给出相应的递归神经网络模块原理图;进而,针对整个闭环系统进行理论分析,证明在一定条件下闭环系统的稳定性;最后,通过两个实例仿真验证所提出方法的有效性.     

基于单网络ADP的一类未知非线性系统的近似最优控制

针对一类未知的连续非线性系统,提出一个基于单网络近似动态规划(ADP)的近似最优控制方案。该方案通过设计一个新型的递归神经网络(RNN)辨识器放松了系统模型需已知或部分已知的要求,并利用一个神经网络(NN)近似系统的性能指标函数消除了常规ADP方法中的控制网络。通过Lyapunov理论分析严格证明了闭环系统内所有信号一致最终有界,并且所获得的性能指标函数和控制输入分别收敛到最优性能指标函数和最优控制输入的小邻域内。仿真结果验证了所提出控制方案的有效性。     

结构振动的时滞输出反馈控制器设计

研究结构振动的时滞输出反馈控制,通过部分可测输出量实现整个系统的主动振动控制．首先将系统的运动微分方程改写成状态空间模型,其控制输入中存在时滞．再利用一个线性项加积分项的变换将原时滞输入系统转化成无时滞的形式．在此基础上,应用输出反馈原理和合理的性能指标设计出系统的控制律．最后以一个三层建筑结构为例,研究系统在地震载荷下的动态响应．在数值计算中,时滞量取为采样周期的整数倍,积分步长取为采样周期．仿真结果表明,本文提出的时滞输出反馈控制律是有效且实用的．     

二次型最优控制问题中的权矩阵与最优控制律

二次型最优的权矩阵选择是一个包含大量经验与技巧的问题．对此，研究权矩阵与最优控制律的关系：一个最优控制律，其对应的性能指标（权矩阵）是否唯一的问题．不论是单输入还是多输入情形，在系统能控性指数大于2，对应权矩阵的对角线元素有2个不为零的元素，且满足一定条件时．该性能指标对应的最优控制律，必有另一性能指标与之对应．     

网络控制系统中通信信道受限对LQG最优控制性能影响

针对一类通信信道受限的多输入多输出网络控制系统(NCSs),研究有限通信系统资源对LOG最优控制性能的影响.对于任一时刻只允许部分传感器和执行器访问网络情况,引入输入、输出通信序列矩阵,建立系统模型;并给出保证系统能控能观的通信序列选取原则;由此设计LQG最优控制算法,定义通信信道不受限和受限情况下目标代价函数的比值为控制性能指标,来评估控制作用的运行效果;通过仿真实验分析了不同信道受限程度对LQG最优控制性能的影响.     

基于切换次序参数化的时滞切换正系统最优控制

考虑时滞线性自治切换正系统,将切换次序参数化作为系统的离散输入,通过系统的等价转换,分析时滞线性自治切换正系统的最优控制问题.利用极小值原理,给出满足性能指标的最优切换次序条件,分析时滞项对性能指标和切换时刻的影响,最后给出数值例子验证结论的有效性.     

控制能量约束时不稳定过程最优控制与仿真

在最优控制问题的研究中,工业过程控制领域中不稳定系统的控制难度比较大,且在许多控制系统设计中控制能量可能成为重要的性能指标。对控制能量存在约束时不稳定过程的最优控制问题进行了研究与仿真,优化问题的难点在于性能指标的表示与最小化。首先基于不稳定过程的互质分解,由敏感度函数和控制敏感度函数定义了一个包含跟踪误差和控制能量在内的性能指标,采用谱分解最小化该性能指标,从而为不稳定系统导出了一种最优的控制器设计方法,可使系统获得最优的控制性能。仿真结果进一步说明了方法的有效性。     

多机电力系统分散最优励磁控制器研究

本文根据有控制结构约束的分散控制理论研究了电力系统分散最优励磁控制,并采用系统的性能指标确定反馈信号以及控制器安装顺序。为了验证所提控制方案对于抑制系统振荡及提高系统稳定性的效益,对一个三机系统做了动态物理模型实验及数字仿真。     

几类协调控制问题及其应用

从3个方面回顾讨论了关联系统协调控制问题,指出了其中存在的一些复杂而有意义的课题。首先对多输入耦合控制系统,讨论了多冗余输入在最优控制中的作用,给出了一个最优指标严格下降的充分必要条件。其次对于一个由2个子系统组成的关联系统讨论了关联项的作用,通过例子说明了在一定的关联结构下,要使整个系统稳定必须有部分子系统不稳定,这充分体现了关联的作用。最后讨论了复杂网络同步中的协调控制问题,分别从图论、节点动力学与内关联函数、网络传递函数H2品质等方面讨论了改善同步的方法,并且指出可以在统一框架下研究多智能体一致性与复杂网络同步问题。     

基于ADP算法的带时滞及饱和的非线性系统最优控制

针对控制时滞及带饱和的一类离散时间非线性系统的最优控制问题,通过重构性能指标函数和对应的系统变换,处理了性能指标函数中的控制耦合项;继而引入一个合适的泛函,解决了控制带饱和问题.给出了一个新的性能指标函数,利用迭代自适应动态规划(ADP)算法获得最优控制.为实现该算法,采用神经网络逼近函数来求解最优控制问题.仿真结果验证了方法的有效性.     

The effects of redundant control inputs in optimal control

For a stabilizable system, the extension of the control inputs has no use for stabilizability, but it is important for optimal control. In this paper, a necessary and sufficient condition is presented to strictly decrease the quadratic optimal performance index after control input extensions. A similar result is also provided for H ₂ optimal control problem. These results show an essential difference between single-input and multi-input control systems. Several examples are taken to illustrate related problems.     

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.     

基于自适应动态规划的非线性鲁棒近似最优跟踪控制

为克服现有近似最优跟踪控制方法只能跟踪连续可微参考输入的局限,本文针对一类具有未知动态的连续时间非线性时不变仿射系统,提出了一种新的基于自适应动态规划的鲁棒近似最优跟踪控制方法.首先采用递归神经网络建立系统模型,然后建立评价神经网络对最优性能指标进行估计,从而得到最优性能指标偏导数的估计值,进而得到近似最优跟踪控制器,最后利用系统输出与参考输入之间的跟踪误差设计鲁棒项对神经网络建模误差进行补偿.分别针对两个非线性系统进行仿真实验,仿真结果表明了所提方法的有效性和优越性.     

On near optimal neural control of multiple-input nonlinear systems

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.     

Model predictive control for hybrid vehicle ecological driving using traffic signal and road slope information

This paper presents development of a control system for ecological driving of a hybrid vehicle. Prediction using traffic signal and road slope information is considered to improve the fuel economy. It is assumed that the automobile receives traffic signal information from intelligent transportation systems(ITS). Model predictive control is used to calculate optimal vehicle control inputs using traffic signal and road slope information. The performance of the proposed method was analyzed through computer simulation results. Both the fuel economy and the driving profile are optimized using the proposed approach. It was observed that fuel economy was improved compared with driving of a typical human driving model.     

Optimum design of linear multivariate sampled-data control systems†

This paper deals with the optimum design of linear multivariate sampled-data control systems,

Section 2 is concerned with the design of such control systems which are optimum on the basis of deadbeat performance. This design procedure is general and can be applied similarly to any deterministic inputs such as step, ramp, etc.

Section 3 is concerned with such control systems with respect to an integral form performance criterion. It is desired that the performance index takes the form of an integral, especially when the state variables of a control system are continuous with respect to time. For this reason, the minimum integral control is considered here.

The performance limits for such systems optimized for a deterministic input are considered in §4, and some interesting theorems are proved by using the w-transform.     

一类参数线性系统辨识的最优输入设计

对未知参数进行估计时,得到的结果与激励系统所选用的输入信号有较大的关系.针对一类参数可线性化系统,本文提出了一种利用多维同步正交信号和直接配点法设计最优输入信号的方法.首先根据最小二乘原理,利用法矩阵构造Mayer型性能指标函数.然后利用不同频率的正弦基函数构造相互正交的多维输入,通过添加幅值与相位的等式约束,使得输入信号在初/末时刻取值均为零.之后采用直接配点法离散状态变量,将动态的最优输入问题转化为静态的非线性规划问题.最后采用从可行解到优化解的串行优化策略进行求解,不仅提高了寻优效率,还确保了优化结果为原问题的可行解.仿真结果表明,与工程上常用的输入信号相比,本文方法获取的最优输入信号可以提高参数估计精度并加快收敛速率.     

能适应多种输入的有限拍鲁棒预检控制系统*

本文主要研究有多种不同形式的输入交替作用于系统时,保证系统具有有限拍最快响应的问题。为了进一步改善系统性能,引入了预检控制(prcview control)概念,并结合作者已获得的部分鲁棒性结果,提出了一种新的能适应多种输入,具有强鲁棒性的有限拍预检挖制器的设计方法。仿真结果表明,该设计法是行之有效的。     

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.