具有网络诱导乘性噪声的线性离散时间控制系统分析与设计

发布时间：2018-08-07 12:29

【摘要】：具有乘性噪声的线性系统是一类特殊的随机系统,相对典型的确定性线性系统而言,它描述了更为广泛的一类实际过程,其控制问题在航天、化学反应、经济、机械等系统中有着广泛的应用。对于线性系统而言,乘性噪声给系统带来了非线性性质,其存在可能改变系统的稳定性,所以相对于常规的具有加性噪声的控制问题,具有乘性噪声的控制问题处理起来更加困难。至目前为止,一些具有乘性噪声的随机系统的镇定和最优控制方面的问题仍然没有彻底解决。因此,在过去的几十年,具有乘性噪声的控制问题一直是广受关注的研究课题。在最近蓬勃发展的网络化控制系统中,乘性噪声模型为描述网络系统通信信道特征比如丢包、量化误差、信道衰退、具有信噪比和带宽受限的约束等提供了一种有效的途径,相应的网络控制问题可被建模为具有网络诱导乘性噪声的随机控制问题,进而可把随机控制理论中的相关工具用于此类问题的研究。本文主要考虑具有网络诱导乘性噪声的线性离散时间系统的均方随机输入输出稳定、均方可镇定、均方H2最优控制与线性二次调节器(Linear Quadratic Regulator, LQR)最优调节、多输出系统的均方可检测以及对周期方波信号的跟踪等问题。本文研究的内容主要集中在以下五个方面：一是研究了基于量化控制信号的网络化控制系统的稳定性问题。考虑最一般结构的网络化反馈控制系统,与系统输出相关的控制信号通过网络传送并作用于一个不稳定的被控对象。通信网络被模型化为对数量化器和无噪声理想信道两部分,将量化误差看成白噪声,所研究系统本质上等效为具有网络诱导乘性噪声的随机系统。与现有文献不同的是,本研究运用系统传递函数互质分解技术,通过Youla参数化方法设计输出反馈控制器,并运用随机小增益定理,得到了系统均方稳定的充分必要条件。该结论给出了确保系统均方随机输入输出稳定的量化误差的方差上界,并表明该上界值仅取决于被控对象的不稳定模态。二是研究了具有控制信号数据包丢失的多输入多输出(Multiple-Input Multiple-Output, MIMO)线性时不变(Linear Time Invariant, LTI)系统输出反馈均方可镇定问题。与系统输出相关的各个控制信号分量通过各自具有数据包丢失的网络传送并作用于被控对象。考虑两种特殊情况：一是具有相对度为1且每一个非最小相位零点均分别与一个控制输入通道相关的非最小相位系统,二是具有相对度为1的最小相位系统。对于前者,基于互质分解的Youla参数化方法设计均方可镇定控制器,在被控对象互质分解的结构上采用被称为上三角互质分解的新方案,得到了用网络信道的信噪比(Signal Noise Ratio, SNR)和系统特征量来刻画的系统均方可镇定的充分条件。即保证系统输出反馈均方可镇定必须要求各个子信道信道容量大于一个临界(下界)值。对于后者,给出了保证系统均方可镇定的最小信道总容量以及在各个子信道间的容量分配关系。该结论表明系统输出反馈均方可镇定要求的信道最小总容量必须大于一个最小值,且该值完全由系统的不稳定模态乘积确定。三是研究了具有状态和控制乘性噪声的网络化线性离散时间系统状态反馈H2最优控制和LQR最优调节问题。利用乘性噪声模型来描述系统存在的量化误差和(或)通信信道不确定性,把具有量化器(或者输入乘性噪声)的网络化反馈控制系统转化为具有网络诱导乘性噪声的随机系统。对于H2最优控制问题,运用随机小增益定理,得到了决定系统状态反馈最优控制器增益的一修正的代数黎卡提方程(Modified Algebraic Riccati equation, MARE)可解的充分必要条件,并给出了最优状态反馈阵的设计方法。对于LQR最优调节问题,以二次成本函数作为系统性能指标,运用随机小增益定理,得到了决定系统状态反馈最优调节控制器增益的一修正的代数黎卡提方程(MARE)可解的充分必要条件,并给出了最优状态反馈阵的设计方法。最后,通过对两个推论的数值仿真,验证了所提出的结论的正确性。四是研究了具有网络诱导乘性噪声信道的离散时间多输出系统均方可检测问题。将输出信道的不可靠性建模成白噪声过程。对于单个数据包传输情形,采用二分法技术,给出为确保网络系统均方可检测的临界(下界)均方容量；对于多个平行数据包传输情形,基于网络资源在所有输出信道中可任意分配假设下,给出用系统的Mahler测度或拓扑熵表示的网络化系统均方可检测的充分必要条件。最后以在擦除信道和有界扇形不确定信道中的应用对结论进行诠释,研究结果与现有的文献结论一致。结果表明,网络化系统的均方可镇定与可检测性仍然保持着经典控制系统中的对偶关系。五是研究了线性时不变、单变量、离散网络化控制系统对周期信号的跟踪问题。与现有文献考虑的参考输入信号大都为常见的非周期信号(如阶跃信号)所不同的是,本研究参考输入信号是离散时间周期信号,在每个周期中,其波形是重复出现的,相应的每个周期中信号功率也是不变的。因此,研究系统对基于功率谱的参考输入信号功率的响应,系统的跟踪性能通过输入信号与受控对象输出之差的功率来衡量,而最优跟踪性能采用跟踪误差的平均功率来度量。考虑的网络化控制系统仅上行通道存在丢包误差的影响,把丢包过程看作两个信号的合成,一是确定性信号,二是随机过程,进而丢包误差描述为源信号和白噪声之间乘积。根据被控对象和随机过程的性质,采用Parseval等式、维纳-辛钦定理和范数矩阵理论得到该系统跟踪性能极限的下界表达式。仿真结果表明,基于本章所设计的控制器能实现对周期信号的有效跟踪,进而验证了结论的正确性。最后,进一步研究了被控对象Gc的极点、控制器Kf主极点和基波周期N选取对跟踪性能(跟踪误差)的影响。
[Abstract]:Linear systems with multiplicative noise are a special class of stochastic systems. Compared with typical deterministic linear systems, it describes a more extensive class of practical processes. The control problems are widely used in aerospace, chemical, economic, mechanical and other systems. For linear systems, multiplicative noise brings non linear systems to the system. In nature, its existence may change the stability of the system, so it is more difficult to deal with the problem of multiplicative noise control relative to the conventional control problem with additive noise. So far, the problem of the stabilization and optimal control of some stochastic systems with multiplicative noise has not been thoroughly solved. In recent decades, the problem of multiplicative noise control has been a subject of great concern. In the recent flourishing networked control system, the multiplicative noise model provides an effective description of network communication channel characteristics such as packet loss, quantization error, channel decline, SNR and bandwidth constrained constraints. The corresponding network control problem can be modeled as a stochastic control problem with network induced multiplicative noise, and then the related tools in stochastic control theory can be used in the study of such problems. This paper mainly considers the stability of the mean square random input and output of linear discrete time system with network induced multiplicative noise. It is determined that the optimal control of the mean square H2 and the optimal control of the linear two times regulator (Linear Quadratic Regulator, LQR), the mean square detection of the multiple output system and the tracking of the periodic square wave signal. The main contents of this paper are mainly in the following five aspects: first, the stability of the networked control system based on the quantized control signal is studied. A networked feedback control system with the most general structure. The control signals associated with the output of the system are transmitted through the network and acted on an unstable controlled object. The communication network is modeled as a logarithmic quantizer and a noise free ideal channel two parts, and the quantization error is regarded as white noise, and the research system is essentially equivalent. It is a random system with network induced multiplicative noise. Unlike the existing literature, this study uses the system transfer function mutual decomposition technique to design the output feedback controller by Youla parameterization, and uses the random gain theorem to obtain the necessary conditions for the stability of the system. The conclusion is given to ensure the mean square of the system. The variance upper bound of the random input and output is stable, and it is shown that the upper bound is only dependent on the unstable mode of the controlled object. Two the output feedback of the multiple input multiple output (Multiple-Input Multiple-Output, MIMO) linear time invariant (Linear Time Invariant, LTI) system with the control signal packet loss is studied. Each control signal component related to the output of the system is transmitted and acted on the controlled object through a network of data packet loss. Two special cases are considered: one is a non minimum phase system with a relative degree of 1 and each of the non minimum phase zeros are respectively related to a control input channel, and two is a phase. For the minimum phase system with a degree of 1. For the former, the Youla parameterized method based on the mutual qualitative decomposition can be designed to stabilize the controller. A new scheme which is called the upper triangular mutual decomposition is adopted in the structure of the mutually qualitative decomposition of the controlled object. The system is depicted with the signal to noise ratio (Signal Noise Ratio, SNR) and the system characteristic quantity of the network channel. The sufficient conditions for the stabilization of the system, that is, the output feedback of the system is guaranteed to be composed of all subchannels, which must require the capacity of each subchannel to be greater than a critical (lower bound) value. For the latter, the total capacity of the minimum channel and the capacity distribution relationship between the subchannels are given. The conclusion shows that the system output is inverse. The minimum total channel capacity of the feed mean square stabilization requirement must be greater than a minimum value, and the value is completely determined by the system's unstable mode product. Three the state feedback H2 optimal control and the LQR optimal control problem for networked linear discrete time systems with state and control multiplicative noise are studied. The multiplicative noise model is used to describe the problem. A networked feedback control system with quantizer (or input multiplicative noise) is transformed into a stochastic system with network induced multiplicative noise. For the H2 optimal control problem, the stochastic gain theorem is used to determine the optimal controller gain of the system state feedback. A necessary and sufficient condition for the solvable algebraic Riccati equation (Modified Algebraic Riccati equation, MARE) is given, and the design method of the optimal state feedback matrix is given. For the LQR optimal regulation problem, the two cost function is used as the performance index of the system and the stochastic small gain theorem is used to determine the state feedback optimal of the system. The sufficient and necessary conditions for the solvable algebraic Riccati equation (MARE) for the gain of the controller are adjusted and the design method of the optimal state feedback array is given. Finally, the correctness of the proposed conclusion is verified by the numerical simulation of two deductions. Four the discrete time multiple output of the network induced multiplicative noise channel is studied. The unreliability of the system can be detected. The unreliability of the output channel is modeled as a white noise process. For a single packet transmission case, a dichotomy technique is used to ensure that the critical (lower) mean square capacity of the network system is detectable. For multiple parallel packets transmission, network resources are available in all the output channels. Under the assumption of arbitrary allocation, the sufficient and necessary conditions for the detection of a networked system with the Mahler measure or topological entropy of the system are given. Finally, the results are interpreted with the application of the erasing channel and the bounded sector uncertain channel. The results are in agreement with the existing literature conclusions. The results show that the network system is all square. The determination and detectability still maintain the dual relationship in the classical control system. Five is the study of the linear time invariable, single variable, discrete networked control system for the periodic signal tracking problem. A signal is a discrete time periodic signal. In each cycle, its waveform is repeated, and the signal power in each cycle is also constant. Therefore, the system's response to the power spectrum based on the power of the reference input signal is measured by the power of the input signal and the output of the controlled object. The optimal tracking performance is measured by the average power of the tracking error. In the networked control system, only the upstream channel has the influence of the packet loss error, and the packet loss process is regarded as the synthesis of two signals, one is the deterministic signal and the two is a random process, and the packet loss error is described as the product of the source signal and the white noise. The properties of the stochastic process, using the Parseval equation, Wiener simhchin theorem and the norm matrix theory, get the lower bound expression for the tracking performance limit of the system. The simulation results show that the controller designed in this chapter can realize the effective tracking of the periodic signal, and then verify the correctness of the knot theory. Finally, the control object G is further studied. The influence of C poles, controller Kf's main pole and fundamental period N on tracking performance (tracking error) is studied.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB535

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