摘要
近几十年来,随着通信、计算机和控制技术的飞速发展,传统的点对点控制模式已经不能满足不断提高的控制系统性能要求,并使得控制模式向网络化控制模式的转变。网络化控制系统(NCSs)以其布线少、成本低、易于扩展和维护等优点,已在众多领域得到了广泛应用。目前,NCSs的已经成为控制理论研究的一个热点方向。
然而,NCSs在带来众多优点的同时,也带来了许多新的问题和困难,例如网络诱导时延、时序错乱、数据包丢失和量化等。针对这些问题虽然已有不少研究成果,但仍然有许多关键问题尚未解决。特别的,针对具有长时延和时序错乱的NCSs,如何建立能够充分描述时序错乱现象的系统模型以及时延特性参数与系统性能之间的定量关系?针对具有量化和丢包的网络化系统,如何解决具有约束的最优状态估计问题并建立量化密度和丢包概率与估计性能之间的关系?等。本文针对NCSs中的时延、时序错乱、丢包和量化,研究了基于滚动优化策略的状态估计和控制器设计问题。研究工作主要包括：
1.针对具有输入约束和外部扰动的长时延NCSs,提出了一种鲁棒滚动时域H∞控制方法。首先,将时变长时延分解为定常部分和不确定部分,从而将所考虑的NCSs建模为一类离散时间范数有界不确定系统。进而,采用Lyapunov稳定性理论和滚动优化策略,给出了使得闭环NCSs渐近稳定的充分条件,并设计了满足给定扰动抑制水平的预测控制器。最后,通过仿真验证了所提方法的有效性。
2.针对具有随机时延和时序错乱的NCSs,提出了一种滚动时域H∞控制方法。首先,通过在执行器端设计一个逻辑补偿器将接收到的信号进行时序重整,得到执行器将采用的控制输入信号序列并给出了新的概率转移矩阵。从而将闭环NCS建模为一类Markovian跳变时滞系统。基于滚动优化策略,导出了状态反馈控制器的设计方法。所得结果能够有效地消除时序错乱对系统的影响。最后,通过角度定位系统仿真验证了所提方法的有效性。
3.针对具有时变时延和时序错乱的NCSs,提出了切换滚动时域控制和滚动时域H∞控制两种方法解决由网络时延的时变特性引起的指数不确定项和时序错乱问题。在切换滚动时域控制方法中,通过时序重整将闭环NCSs建模为一个具有有限个子系统的切换系统。在滚动时域H∞控制方法中,通过采用执行器读取缓冲区的频率高于传感器采样频率的工作方式,将NCSs建模为一类多速率系统,并进一步将该模型转化为多时滞参数不确定离散时间系统。基于这两种方法给出了系统稳定化控制器的设计方法,并建立了时延变化率与NCSs性能之间的关系。
4.针对具有多数据包丢失的网络化系统,提出了一种能够处理不等式约束的滚动时域估计方法。丢包现象采用一个Bernoulli随机过程描述,采用输入保持策略,将系统描述为一个随机参数化系统模型。基于滚动优化策略,给出了无约束滚动时域估计器。针对噪声存在不等式约束时,给出约束滚动时域估计器的设计方法。进一步,分析了估计器的估计性能,给出了保证估计误差范数有界的充分条件。最后,通过连续搅拌釜式反应器仿真验证了所提方法的有效性。
5.研究了具有随机丢包无线网络化系统的滚动时域SINR估计问题。首先,根据流速控制和功率控制算法,建立了一个dB尺度下无线网络化系统的状态空间模型,导出了SINR水平的上下界约束条件,并将SINR水平的有界约束转化为系统的状态约束。基于滚动优化策略,给出了无约束SINR估计器的解析结构。考虑到状态变量和噪声之间的耦合,提出了一步滚动时域SINR估计算法用于解决SINR约束估计问题。最后,通过无线传感器网络仿真验证了所提方法的有效性。
6.研究了同时具有量化和随机丢包网络化系统的滚动时域估计问题。采用对数量化器和置零策略将系统建模为一个随机参数不确定系统。基于滚动优化策略,求解一个具有不确定参数的最小二次优化问题,分别得到了最优估计器和近似估计器。进而,分析最优估计器的估计性能,建立了量化密度和丢包概率与估计性能之间的关系并给出了保证估计误差上界收敛的最大量化密度和最大丢包概率。最后,通过仿真验证了所提方法的有效性。
In the last few decades, with the rapid developments of communication, computer and control technology, the traditional point-to-point control architecture cannot meet the required performance of control systems and changes to the networked control counterpart. Networked control systems (NCSs) have some nice advantages such as less wiring, low cost, easy maintenance and expanding. Due to these distinctive benefits, NCSs have found applications in a variety of areas. Therefore, NCSs have now been one of the hot research topics in the control society.
However, although NCSs have brought so many advantages, they also bring lots of new problems and difficulties, such as network-induced delays, packet disordering, packet dropouts, quantization, et al. Though there have been fruitful research results on those issues, lots of problems remain to be unsolved. Especially, how to establish a model to de-scribe the phenomenon of packet disordering for NCSs with random or time-vary delay and relations between parameters characterizing the delays and performances? How to solve the optimal state estimation problem with system constraints and establish relations among the quantization density, the packet dropout probability and estimation performances? Based on the moving optimization strategy, the state estimation and controller design problem are respectively investigated for NCSs in this thesis. The main work is summarized as follows:
1. A robust moving horizon H∞control method is proposed for NCSs with long time-delays, input constraints and disturbances. First, the delay is separated into a nominal part and a time-varying uncertain part, and then the NCSs are modeled as a class of uncertain systems with norm-bounded uncertainties. Based on the Lyapunov stability theory and moving optimization strategy, a sufficient condition is obtained such that the closed-loop system is asymptotically stable, and predictive controller is designed with a prescribed H∞performance level. The effectiveness of the proposed method is illustrated by a numerical simulation.
2. A moving horizon H∞control method is proposed for NCSs with random delays and packet disordering. By introducing a logic data packet processor to reorder the packet from the network to actuator, the newest data signal sequence and a new transition proba-bility matrix are obtained, and then the NCSs are modeled as a class of Markovian jump systems. Based on the moving optimization strategy, state feedback controllers are de-signed by the proposed method. The impact of packet disordering on the performance of NCSs is effectively eliminated. The effectiveness of the proposed methods are illustrated by an angular positioning system.
3. A switched moving horizon control method and a moving horizon H∞, control method are proposed for NCSs with time-varying delays and packet disordering, respec-tively. In the switched moving horizon control method, the NCSs are modeled as a class of switched systems by packet disordering. In the moving horizon H∞control method, the actuator reads the buffer periodically at a smaller period than the sensor, and the resulting system is a multi-rate system, and then converted into a parameter uncertain system with multi-step delay. Based on the proposed two methods, state feedback controllers are also designed, and relation between the delay variation rate and system performance is explicitly established for the NCSs.
4. A moving horizon estimation method is proposed to deal with inequality constraints for networked systems with multiple packet dropouts. The packet dropout process is de-scribed a Bernoulli random process. By using hold-input strategy, the networked system is modeled as a stochastic parameter system model. Based on moving optimization strat-egy, the unconstrained optimization estimator is obtained with analytical solution. The design procedure for constrained estimator is presented for networked system with inequal-ity constraint of noises. Moreover, the stability properties of the estimator are studied, and a sufficient condition is obtained to ensure the estimation error to be norm-bounded. The effectiveness of the proposed method is illustrated by a simulation of a continuous stirred tank reactor.
5. The moving horizon SINR estimation problem is investigated for wireless net-worked systems with random packet dropouts. Based on flow-rate and power control algo-rithm, a state-space model is obtained in dB scale for wireless networked system, and the bound constraints of SINR is derived and converted to state constraints. By using moving optimization strategy, the unconstrained SINR estimator is obtained with analytical solu-tion. Considering the coupling of state variable and process noise, a one-step MHE algo-rithm is presented to solve the constrained SINR optimization problem. The effectiveness of the proposed method is illustrated by a numerical simulation.
6. The moving horizon estimation problem is investigated for networked systems with quantized measurements and packet dropouts. By using logarithmic quantizer and zero-input strategy for packet dropouts, the networked system is modeled as a stochastic param-eter uncertain system model. Based on moving optimization strategy, the optimal estima-tor and approximate estimator are obtained by solving a regularized least-squares problem with uncertain parameters. The stability properties of the optimal estimator are also stud-ied. The obtained stability condition implicitly establishes a relation between the upper bound of the estimation error and two parameters, namely, the quantization density and the packet dropout probability. Moreover, the maximum quantization density and the maxi-mum packet dropout probability are given to ensure the convergence of the upper bound of the estimation error sequence. The effectiveness of the proposed method is illustrated by a numerical simulation.
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