信息受限的网络化系统的镇定与控制
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摘要
最近信息受限的控制问题引起大家广泛关注.当控制信号通过一个有限容量的传输信道时,由于带宽限制使得信息只能做到有限精度的传输.在此信道连接下的闭环系统的控制模型与以往的模型很不一样.此时,确定多大的信道容量能够达到控制目标的要求是这一类问题关心的重点.而且,如何合理的设计控制器和加密器来完成控制目标是解决这一类问题的关键.几乎所有这方面的研究工作都集中在正则受控系统.
本文研究了一类信息受限的非线性离散系统的镇定和检测问题;两类信息受限的混沌同步问题和信息受限的奇摄动系统的镇定问题以及奇摄动网络化系统的模型控制.
本文主要做了以下四个方面的工作:
1.一类信息受限的非线性离散系统的镇定和检测问题;
2.两类不同的信息受限的混沌同步问题;
3.信息受限的奇摄动系统的镇定:
4.奇摄动网络化系统的模型控制.
第一.研究了一类非线性离散系统在信息受限下的镇定和检测问题.给出了为实现镇定目标而设计的编码器和解码一控制器以及对信道容量的要求.引入一个辅助系统解决了离散系统中极限无定义的困难,成功将[64]的工作推广到了离散情形.采用线性矩阵不等式的方法给出了该设计方案的一个充分条件.同时,在不考虑控制输入的情况下,得到了关于系统检测的结论.数值模拟说明所给方法的有效性.
第二,研究了离散和连续混沌模型在信息受限下的同步问题.分别就两个具有相同结构但带有不同初值的离散和连续混沌模型,通过一个有限容量的信道相连时.具体给出了其能实现同步误差渐近趋于零的编码器和解码-控制器的设计以及对信道容量的要求.数值模拟说明了所给设计方法的有效性.
第三,研究了线性奇摄动系统在信息受限下的镇定问题。给出了一种与小参数无关的加密器的设计和对信道容量的要求。给出了控制器需要满足的两种不同假设:特别,其中之一说明经典的组合控制仍然成立。利用矩阵的扰动性质和线性奇摄动系统的解耦结构,证明了主要结果。给出的例子说明了结果的有效性。
最后,研究了奇摄动网络化系统的模型控制。利用线性奇摄动系统的解耦性质和矩阵扰动的的相关理论以及矩阵的拉普拉斯变换。我们得到了在小参数足够小时实现指数稳定的条件。并研究了具有短时延的奇摄动网络化系统的模型控制,探讨了其解的表达式和稳定性。给出的数值例子说明了结论的有效性。
受最新的基于观测器的信息受限的混沌同步工作([17])的启发,本文研究了信息受限的混沌同步问题.这是同类问题中为数不多的工作。其次,本文第一次提出了奇摄动网络化控制的问题,并研究了信息受限的线性奇摄动网络化系统的镇定。同时讨论了相应的模型控制,成功地将在正则网络化系统中减少带宽限制行之有效的模型控制方法推广到奇摄动网络化系统中去。
Recently, the problem of control with limited information has attracted significant attentions. Unlike classical control problem, control with limited information concerns the impact of the capacity of a channel on the performance of systems. A natural question to ask is how much capacity is needed to achieve a specified control performance or estimation accuracy. Meanwhile, how to design a suitable quantizer (i.e. coder-decoder pair) and the controller is also a key issue. All most all research works in this regard concentrates on the works of regular plants for networked control systems (NCSs, for short) with limited information.
In this dissertation, we have done in this regard for four different classes of problems as follows:
1. stabilization and detection of a class of nonlinear discrete-time systems with limited information;
2. synchronization of two identically chaotic systems coupled through a limited capacity communication channel (LCCC) for both continuous-time and discrete-time cases;
3. feedback stabilization for linear singularly perturbed systems via a LCCC;
4. model-based control of singularly perturbed networked control systems.
Firstly, the stability of a class of discrete-time systems with Lipschitz nonlinearities via a LCCC is studied. A sufficient condition for the stabilization of the problem is presented in terms of linear matrix inequalities. A stabilizing coder-decoder-controller is constructed and the condition about the channel capacity is derived. In addition, a corollary is deduced with no input from the obtained result on detection for the discrete-time systems. Finally, one example is worked out to illustrate the efficiency and feasibility of the proposed approach. It is worthy to point out that an auxiliary system is introduced to overcome the difficulty when we extend the result of [64] from the continuous time to the discrete one.
Secondly, the problem of synchronization of two identically chaotic systems coupled through a LCCC is addressed. Both the continuous-time and the discrete-time chaos systems are concerned.
For the continuous chaos model, using the sampled and encoded information, an impulsive control designed is applied to the response system by resetting its initial state at the beginning of every sampling interval. A coder-decoder-controller is constructed and the condition about, the channel capacity is derived. Finally, the numerical simulation for the Chua's chaotic system is shown to illustrate the obtained result.
On the other hand, a new control strategy is given for discrete-time chaos synchronization where the drive system and the response system are coupled via a LCCC. One condition about channel capacity is presented to ensure synchronization between the two chaotic systems coupled by a LCCC. Based on this condition, an explicit coder-decoder pair for the coding algorithm is designed. Finally, the proposed control strategy is applied to the well-known Hénon system and the hyperchaotic maps, respectively, and their numerical simulations illustrate the validity of the obtained result.
Thirdly, the state feedback stabilization problems for singularly perturbed linear time-invariant systems (SPLSs for short) via a finite data rate channel using sampled and encoded states is discussed. Taking advantages of the decoupled form of SPLSs and the analysis of matrix perturbation we derive a requirement that defines a bound on the required data rate for the limited data rate network to achieve feedback stabilization. This bound is independent of the small parameter of SPLSs. Based on this requirement, a series of encoding functions and a stabilizing control strategy can be defined in an explicit way. Then, there exists a bound of the small parameter such that SPLSs can be exponentially stabilized under communication constraints by the proposed control strategy for all the small parameter within the desired bound.
Finally, the state feedback control of the linear singularly perturbed plant is studied, where the sensor and the controller/actuator are connected via a network and the transmission frequency is constant. In terms of the model-based control, the model plant in the singularly perturbed system is added at the controller/actuator to stabilize the original singularly perturbed system with periodically updating its state by the actual state of the plant provided by the sensor. Moreover, under some certain conditions, independent of the small parameterε, the existence of the bound of the small parameterεis shown to guarantee the globally exponential stability of the whole closed-loop singularly perturbed system. In addition, a numerical simulation is shown to illustrate the results of the paper. Next, we extend our results to include the case where the transmission delay is present. A new error model is proposed and the response of the system is shown as well as the stability of the system is analyzed.
In summary, inspired by the work of ([17]) based on observer, the synchronization of two identically chaotic systems with limited information has been successfully investigated. There have been a few works so far in this direction. For NCSs with the plant having singular perturbation structure, this is a first time to be addressed. We solve feedback stabilization of this problem. Moreover, we also extend the model-based approach, which is shown effective to reduce bandwidth restriction for NCSs with regular plant, to the case with plant that is SPLSs.
本文研究了一类信息受限的非线性离散系统的镇定和检测问题;两类信息受限的混沌同步问题和信息受限的奇摄动系统的镇定问题以及奇摄动网络化系统的模型控制.
本文主要做了以下四个方面的工作:
1.一类信息受限的非线性离散系统的镇定和检测问题;
2.两类不同的信息受限的混沌同步问题;
3.信息受限的奇摄动系统的镇定:
4.奇摄动网络化系统的模型控制.
第一.研究了一类非线性离散系统在信息受限下的镇定和检测问题.给出了为实现镇定目标而设计的编码器和解码一控制器以及对信道容量的要求.引入一个辅助系统解决了离散系统中极限无定义的困难,成功将[64]的工作推广到了离散情形.采用线性矩阵不等式的方法给出了该设计方案的一个充分条件.同时,在不考虑控制输入的情况下,得到了关于系统检测的结论.数值模拟说明所给方法的有效性.
第二,研究了离散和连续混沌模型在信息受限下的同步问题.分别就两个具有相同结构但带有不同初值的离散和连续混沌模型,通过一个有限容量的信道相连时.具体给出了其能实现同步误差渐近趋于零的编码器和解码-控制器的设计以及对信道容量的要求.数值模拟说明了所给设计方法的有效性.
第三,研究了线性奇摄动系统在信息受限下的镇定问题。给出了一种与小参数无关的加密器的设计和对信道容量的要求。给出了控制器需要满足的两种不同假设:特别,其中之一说明经典的组合控制仍然成立。利用矩阵的扰动性质和线性奇摄动系统的解耦结构,证明了主要结果。给出的例子说明了结果的有效性。
最后,研究了奇摄动网络化系统的模型控制。利用线性奇摄动系统的解耦性质和矩阵扰动的的相关理论以及矩阵的拉普拉斯变换。我们得到了在小参数足够小时实现指数稳定的条件。并研究了具有短时延的奇摄动网络化系统的模型控制,探讨了其解的表达式和稳定性。给出的数值例子说明了结论的有效性。
受最新的基于观测器的信息受限的混沌同步工作([17])的启发,本文研究了信息受限的混沌同步问题.这是同类问题中为数不多的工作。其次,本文第一次提出了奇摄动网络化控制的问题,并研究了信息受限的线性奇摄动网络化系统的镇定。同时讨论了相应的模型控制,成功地将在正则网络化系统中减少带宽限制行之有效的模型控制方法推广到奇摄动网络化系统中去。
Recently, the problem of control with limited information has attracted significant attentions. Unlike classical control problem, control with limited information concerns the impact of the capacity of a channel on the performance of systems. A natural question to ask is how much capacity is needed to achieve a specified control performance or estimation accuracy. Meanwhile, how to design a suitable quantizer (i.e. coder-decoder pair) and the controller is also a key issue. All most all research works in this regard concentrates on the works of regular plants for networked control systems (NCSs, for short) with limited information.
In this dissertation, we have done in this regard for four different classes of problems as follows:
1. stabilization and detection of a class of nonlinear discrete-time systems with limited information;
2. synchronization of two identically chaotic systems coupled through a limited capacity communication channel (LCCC) for both continuous-time and discrete-time cases;
3. feedback stabilization for linear singularly perturbed systems via a LCCC;
4. model-based control of singularly perturbed networked control systems.
Firstly, the stability of a class of discrete-time systems with Lipschitz nonlinearities via a LCCC is studied. A sufficient condition for the stabilization of the problem is presented in terms of linear matrix inequalities. A stabilizing coder-decoder-controller is constructed and the condition about the channel capacity is derived. In addition, a corollary is deduced with no input from the obtained result on detection for the discrete-time systems. Finally, one example is worked out to illustrate the efficiency and feasibility of the proposed approach. It is worthy to point out that an auxiliary system is introduced to overcome the difficulty when we extend the result of [64] from the continuous time to the discrete one.
Secondly, the problem of synchronization of two identically chaotic systems coupled through a LCCC is addressed. Both the continuous-time and the discrete-time chaos systems are concerned.
For the continuous chaos model, using the sampled and encoded information, an impulsive control designed is applied to the response system by resetting its initial state at the beginning of every sampling interval. A coder-decoder-controller is constructed and the condition about, the channel capacity is derived. Finally, the numerical simulation for the Chua's chaotic system is shown to illustrate the obtained result.
On the other hand, a new control strategy is given for discrete-time chaos synchronization where the drive system and the response system are coupled via a LCCC. One condition about channel capacity is presented to ensure synchronization between the two chaotic systems coupled by a LCCC. Based on this condition, an explicit coder-decoder pair for the coding algorithm is designed. Finally, the proposed control strategy is applied to the well-known Hénon system and the hyperchaotic maps, respectively, and their numerical simulations illustrate the validity of the obtained result.
Thirdly, the state feedback stabilization problems for singularly perturbed linear time-invariant systems (SPLSs for short) via a finite data rate channel using sampled and encoded states is discussed. Taking advantages of the decoupled form of SPLSs and the analysis of matrix perturbation we derive a requirement that defines a bound on the required data rate for the limited data rate network to achieve feedback stabilization. This bound is independent of the small parameter of SPLSs. Based on this requirement, a series of encoding functions and a stabilizing control strategy can be defined in an explicit way. Then, there exists a bound of the small parameter such that SPLSs can be exponentially stabilized under communication constraints by the proposed control strategy for all the small parameter within the desired bound.
Finally, the state feedback control of the linear singularly perturbed plant is studied, where the sensor and the controller/actuator are connected via a network and the transmission frequency is constant. In terms of the model-based control, the model plant in the singularly perturbed system is added at the controller/actuator to stabilize the original singularly perturbed system with periodically updating its state by the actual state of the plant provided by the sensor. Moreover, under some certain conditions, independent of the small parameterε, the existence of the bound of the small parameterεis shown to guarantee the globally exponential stability of the whole closed-loop singularly perturbed system. In addition, a numerical simulation is shown to illustrate the results of the paper. Next, we extend our results to include the case where the transmission delay is present. A new error model is proposed and the response of the system is shown as well as the stability of the system is analyzed.
In summary, inspired by the work of ([17]) based on observer, the synchronization of two identically chaotic systems with limited information has been successfully investigated. There have been a few works so far in this direction. For NCSs with the plant having singular perturbation structure, this is a first time to be addressed. We solve feedback stabilization of this problem. Moreover, we also extend the model-based approach, which is shown effective to reduce bandwidth restriction for NCSs with regular plant, to the case with plant that is SPLSs.
引文
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