具有網絡誘導乘性噪聲的線性離散時間控制系統(tǒng)分析與設計
發(fā)布時間：2018-08-07 12:29
【摘要】：具有乘性噪聲的線性系統(tǒng)是一類特殊的隨機系統(tǒng),相對典型的確定性線性系統(tǒng)而言,它描述了更為廣泛的一類實際過程,其控制問題在航天、化學反應、經濟、機械等系統(tǒng)中有著廣泛的應用。對于線性系統(tǒng)而言,乘性噪聲給系統(tǒng)帶來了非線性性質,其存在可能改變系統(tǒng)的穩(wěn)定性,所以相對于常規(guī)的具有加性噪聲的控制問題,具有乘性噪聲的控制問題處理起來更加困難。至目前為止,一些具有乘性噪聲的隨機系統(tǒng)的鎮(zhèn)定和最優(yōu)控制方面的問題仍然沒有徹底解決。因此,在過去的幾十年,具有乘性噪聲的控制問題一直是廣受關注的研究課題。在最近蓬勃發(fā)展的網絡化控制系統(tǒng)中,乘性噪聲模型為描述網絡系統(tǒng)通信信道特征比如丟包、量化誤差、信道衰退、具有信噪比和帶寬受限的約束等提供了一種有效的途徑,相應的網絡控制問題可被建模為具有網絡誘導乘性噪聲的隨機控制問題,進而可把隨機控制理論中的相關工具用于此類問題的研究。本文主要考慮具有網絡誘導乘性噪聲的線性離散時間系統(tǒng)的均方隨機輸入輸出穩(wěn)定、均方可鎮(zhèn)定、均方H2最優(yōu)控制與線性二次調節(jié)器(Linear Quadratic Regulator, LQR)最優(yōu)調節(jié)、多輸出系統(tǒng)的均方可檢測以及對周期方波信號的跟蹤等問題。本文研究的內容主要集中在以下五個方面：一是研究了基于量化控制信號的網絡化控制系統(tǒng)的穩(wěn)定性問題�？紤]最一般結構的網絡化反饋控制系統(tǒng),與系統(tǒng)輸出相關的控制信號通過網絡傳送并作用于一個不穩(wěn)定的被控對象。通信網絡被模型化為對數量化器和無噪聲理想信道兩部分,將量化誤差看成白噪聲,所研究系統(tǒng)本質上等效為具有網絡誘導乘性噪聲的隨機系統(tǒng)。與現(xiàn)有文獻不同的是,本研究運用系統(tǒng)傳遞函數互質分解技術,通過Youla參數化方法設計輸出反饋控制器,并運用隨機小增益定理,得到了系統(tǒng)均方穩(wěn)定的充分必要條件。該結論給出了確保系統(tǒng)均方隨機輸入輸出穩(wěn)定的量化誤差的方差上界,并表明該上界值僅取決于被控對象的不穩(wěn)定模態(tài)。二是研究了具有控制信號數據包丟失的多輸入多輸出(Multiple-Input Multiple-Output, MIMO)線性時不變(Linear Time Invariant, LTI)系統(tǒng)輸出反饋均方可鎮(zhèn)定問題。與系統(tǒng)輸出相關的各個控制信號分量通過各自具有數據包丟失的網絡傳送并作用于被控對象�？紤]兩種特殊情況：一是具有相對度為1且每一個非最小相位零點均分別與一個控制輸入通道相關的非最小相位系統(tǒng),二是具有相對度為1的最小相位系統(tǒng)。對于前者,基于互質分解的Youla參數化方法設計均方可鎮(zhèn)定控制器,在被控對象互質分解的結構上采用被稱為上三角互質分解的新方案,得到了用網絡信道的信噪比(Signal Noise Ratio, SNR)和系統(tǒng)特征量來刻畫的系統(tǒng)均方可鎮(zhèn)定的充分條件。即保證系統(tǒng)輸出反饋均方可鎮(zhèn)定必須要求各個子信道信道容量大于一個臨界(下界)值。對于后者,給出了保證系統(tǒng)均方可鎮(zhèn)定的最小信道總容量以及在各個子信道間的容量分配關系。該結論表明系統(tǒng)輸出反饋均方可鎮(zhèn)定要求的信道最小總容量必須大于一個最小值,且該值完全由系統(tǒng)的不穩(wěn)定模態(tài)乘積確定。三是研究了具有狀態(tài)和控制乘性噪聲的網絡化線性離散時間系統(tǒng)狀態(tài)反饋H2最優(yōu)控制和LQR最優(yōu)調節(jié)問題。利用乘性噪聲模型來描述系統(tǒng)存在的量化誤差和(或)通信信道不確定性,把具有量化器(或者輸入乘性噪聲)的網絡化反饋控制系統(tǒng)轉化為具有網絡誘導乘性噪聲的隨機系統(tǒng)。對于H2最優(yōu)控制問題,運用隨機小增益定理,得到了決定系統(tǒng)狀態(tài)反饋最優(yōu)控制器增益的一修正的代數黎卡提方程(Modified Algebraic Riccati equation, MARE)可解的充分必要條件,并給出了最優(yōu)狀態(tài)反饋陣的設計方法。對于LQR最優(yōu)調節(jié)問題,以二次成本函數作為系統(tǒng)性能指標,運用隨機小增益定理,得到了決定系統(tǒng)狀態(tài)反饋最優(yōu)調節(jié)控制器增益的一修正的代數黎卡提方程(MARE)可解的充分必要條件,并給出了最優(yōu)狀態(tài)反饋陣的設計方法。最后,通過對兩個推論的數值仿真,驗證了所提出的結論的正確性。四是研究了具有網絡誘導乘性噪聲信道的離散時間多輸出系統(tǒng)均方可檢測問題。將輸出信道的不可靠性建模成白噪聲過程。對于單個數據包傳輸情形,采用二分法技術,給出為確保網絡系統(tǒng)均方可檢測的臨界(下界)均方容量；對于多個平行數據包傳輸情形,基于網絡資源在所有輸出信道中可任意分配假設下,給出用系統(tǒng)的Mahler測度或拓撲熵表示的網絡化系統(tǒng)均方可檢測的充分必要條件。最后以在擦除信道和有界扇形不確定信道中的應用對結論進行詮釋,研究結果與現(xiàn)有的文獻結論一致。結果表明,網絡化系統(tǒng)的均方可鎮(zhèn)定與可檢測性仍然保持著經典控制系統(tǒng)中的對偶關系。五是研究了線性時不變、單變量、離散網絡化控制系統(tǒng)對周期信號的跟蹤問題。與現(xiàn)有文獻考慮的參考輸入信號大都為常見的非周期信號(如階躍信號)所不同的是,本研究參考輸入信號是離散時間周期信號,在每個周期中,其波形是重復出現(xiàn)的,相應的每個周期中信號功率也是不變的。因此,研究系統(tǒng)對基于功率譜的參考輸入信號功率的響應,系統(tǒng)的跟蹤性能通過輸入信號與受控對象輸出之差的功率來衡量,而最優(yōu)跟蹤性能采用跟蹤誤差的平均功率來度量�？紤]的網絡化控制系統(tǒng)僅上行通道存在丟包誤差的影響,把丟包過程看作兩個信號的合成,一是確定性信號,二是隨機過程,進而丟包誤差描述為源信號和白噪聲之間乘積。根據被控對象和隨機過程的性質,采用Parseval等式、維納-辛欽定理和范數矩陣理論得到該系統(tǒng)跟蹤性能極限的下界表達式。仿真結果表明,基于本章所設計的控制器能實現(xiàn)對周期信號的有效跟蹤,進而驗證了結論的正確性。最后,進一步研究了被控對象Gc的極點、控制器Kf主極點和基波周期N選取對跟蹤性能(跟蹤誤差)的影響。
[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.
【學位授予單位】：華南理工大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TB535
本文編號：2170027
[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.
【學位授予單位】：華南理工大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TB535
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