混杂动态系统的预测控制器设计与性能分析
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摘要
许多复杂的生产过程不仅包含了连续的物理、化学和生物反应,而且受到大量的逻辑规则约束、不同操作模式间的切换、人为指令等影响,表现出一种混杂动态特性。对于这类同时存在连续变量动态与离散事件动态,以及动态之间相互影响、相互作用的复杂系统称为混杂动态系统。由于混杂动态系统本质上是非线性的、甚至是不光滑的,使得其控制问题,特别是具有约束情况下的控制非常困难。预测控制能有效地处理约束、不确定性和时滞等问题,并且具有对模型的宽容性、有限时域滚动优化的有效性等特点,为混杂动态系统控制开辟了一条重要途径。本文采用预测控制方法,对带有混杂动态特性的系统进行控制器设计、优化问题求解以及系统性能分析等方面的探讨和研究。
本文的主要内容包括:
针对离散时间分段线性(piecewise linear,PWL)系统,考虑实际控制问题中存在模型不确定性和外界干扰的情况,提出了附加干扰项和凸多面体两种形式描述的不确定离散时间PWL系统的预测控制器设计方法。对带有附加干扰项的PWL系统,通过加紧标称PWL系统预测控制优化问题的约束条件,刻画外界干扰对系统的影响程度,从而给出了紧约束预测控制方法。所设计的预测控制器在保证闭环系统鲁棒可行性和收敛性的同时,降低了计算的复杂度。对于PWL系统具有多面体不确定性的情况,利用无穷时域预测控制策略,通过在线求解线性矩阵不等式,提出了鲁棒预测控制器的设计方法,在此基础上,给出了一种改进的在线离线相结合的鲁棒预测控制方法,以减少算法的计算量。
研究连续时间PWL系统的控制问题,提出了具有稳定性保证的混合预测控制器设计方法。首先,针对每一个子模态,分别设计有界控制器和预测控制器,并构造出连续时间PWL系统的稳定域估计集。然后,在稳定域估计集内,提出了一种基于预测控制和有界控制的混合控制切换策略,使得每个子模态在保证稳定性的同时,最优性也得到改善。在此基础上,利用多Lyapunov函数方法,保证了不同子模态之间切换的稳定性。该方法只需要针对每个子模态计算二次规划,不必对整个PWL系统求解定性和定量双重指标下的优化问题,降低了优化问题的计算复杂度。
网络控制系统是一类典型的具有混杂动态特性的系统,在运行的过程中不可避免地包含相互作用的离散和连续动态,因此,可以利用混杂动态系统控制理论和方法去解决网络控制系统中遇到的问题。采用多速率模式描述网络控制系统,可以减少由于网络拥塞而造成的信息丢失,得到更好的系统响应。针对输出采样周期是输入更新周期整数倍的多速率网络控制系统,将其建模为切换系统,给出了稳定性充分条件,并利用预测控制中的未来控制序列,对快速率控制律进行补偿,设计了依赖系统状态的能够镇定多速率网络控制系统的预测控制器。所提出的可镇定预测控制与传统的预测控制相比,可以有效地补偿网络诱导时滞对系统的影响。
网络带宽资源的限制,会产生网络诱导时滞、数据包丢失等问题,从而导致被控系统的性能降低甚至使系统失稳。为解决这一问题,一方面可以从系统设计的角度出发,对网络诱导时滞和丢包进行补偿。另一方面,可以从改善网络通讯性能出发,通过对网络通讯资源进行合理地分配和调度,降低网络带宽资源限制发生的可能性。从系统设计的角度出发,提出了一种多速率滚动时域状态估计器,以克服网络诱导时滞的影响,并对估计器的稳定性和无偏性进行了分析,给出当系统干扰有界情况下估计误差的上界。考虑到网络通讯约束对网络控制系统的影响,从改善网络通讯性能出发,通过引入逻辑变量组成的通讯调度矩阵,将多速率网络控制闭环系统建模为混合逻辑动态系统,提出了一种可镇定预测控制器设计方法。这种预测控制方法,在每个慢采样时刻,通过求解混合整数二次规划问题,得到一组稳定的快速率控制律,同时也得到了相应的网络调度策略。
Many complex processes not only include continuous physical, chemical and biologic reaction, but also are influenced by logic constraints, switching between different operating modes and human command, exhibiting hybrid dynamical characteristics. A class of complex systems in which continuous dynamic behavior and discrete dynamic behavior interact are called hybrid dynamical systems. The nonlinearity and even nonsmoothness of hybrid dynamical systems in nature make the problems of controller design and analysis very difficult, especially the case with constraints. Predictive control can deal with constraints, uncertainties and time delays. Also, it has the tolerance of model applied for prediction and efficiency of finite receding horizon optimization. Therefore, this methodology provides an important way for the control of hybrid dynamical systems. In this dissertation, predictive control is employed for hybrid dynamical systems, and the controller synthesis, the solution of optimization and the analysis of system performance are studied. The main contents are as follows.
Predictive controller design methods for discrete time piecewise linear (PWL) systems are studied in consideration of the modeling uncertainty and disturbances. For PWL systems with constraints and persistent, unknown but bounded disturbances, a constraints tightening robust predictive controller is presented. Based on optimization problem of predictive control for nominal PWL systems, the constraints are tightened to overcome the influence of persistent bounded disturbances. The proposed predictive controller can guarantee robust feasibility and convergence of closed-loop PWL systems, and reduce the complexity of computation. For uncertain structure of PWL systems that is described by a set of polytopic parameter varying models, an infinite horizon on-line predictive control technique for guaranteeing robust stability is developed by solving linear matrix matrices (LMIs). On the basis of the on-line algorithm, an improved algorithm is proposed to reduce computation.
For continuous-time PWL systems, a mixed predictive control strategy is proposed to guarantee global stability. For each mode of PWL systems, a bounded controller and a predictive controller are designed respectively, and a stable estimation region of PWL systems is developed. In the stable estimation region, a mixed control switching strategy based on predictive control and bounded control is given for each mode to achieve the reconciliation of stability and optimality properties. With the switching rules of different modes of PWL systems, the global stability can be guaranteed. In the proposed method, only quadratic programming problems are computed, which reduces on-line complexity of the optimization of hybrid dynamical systems.
As a class of hybrid dynamical systems, networked control systems (NCSs) include interacting discrete and continuous dynamical characteristics. Thus, hybrid systems control theory and approaches can be used in the control of NCSs. Using multirate scheme to describe NCSs can reduce the loss of information caused by network congestion, and can get a good response. For multirate networked control systems (MNCSs) with the output sampling period several times larger than the input updating period, we can use predictive control strategy to generate a set of future control sequences to compensate for the network-induced time delays. The closed-loop MNCSs are described as switched systems. Sufficient stability conditions are established via a switched Lyapunov function approach. Then, a predictive controller dependent on state for stabilizing MNCSs is proposed based on a finite input and state horizon cost with a finite terminal weighting matrix. Compared with traditional predictive control, the proposed stabilizing predictive control strategy can compensate for the influence of network-induced time delays.
Limited capacity for transmission of NCSs can lead to network-induced time delays, data losses and other problems, which can reduce systems performance and even destabilize systems. In order to overcome these problems, there are two approaches: (i) The influence of network-induced time delays and data packet loss can be compensated by system synthesis. (ii) The communication property can be improved by reasonable allocation and scheduling of network communication resources. From the perspective of systems synthesis, a receding horizon state estimation is proposed for MNCSs to overcome the influence of network-induced time delays. Convergence results and unbiasedness properties are analyzed. An upper bound of estimation error is presented under the assumption of bounded disturbances acting on the system and measurement equations. Taking the influence of communication constraints into account, from the perspective of improving communication performance, a communication scheduling matrix is introduced to describe possible scheduling, and the closed-loop MNCSs can be modeled as mixed logic dynamical systems. A predictive controller is designed by solving a mixed integer quadratic programming problem, which not only can stabilize closed-loop systems but also can present dynamical scheduling of communication channels.
本文的主要内容包括:
针对离散时间分段线性(piecewise linear,PWL)系统,考虑实际控制问题中存在模型不确定性和外界干扰的情况,提出了附加干扰项和凸多面体两种形式描述的不确定离散时间PWL系统的预测控制器设计方法。对带有附加干扰项的PWL系统,通过加紧标称PWL系统预测控制优化问题的约束条件,刻画外界干扰对系统的影响程度,从而给出了紧约束预测控制方法。所设计的预测控制器在保证闭环系统鲁棒可行性和收敛性的同时,降低了计算的复杂度。对于PWL系统具有多面体不确定性的情况,利用无穷时域预测控制策略,通过在线求解线性矩阵不等式,提出了鲁棒预测控制器的设计方法,在此基础上,给出了一种改进的在线离线相结合的鲁棒预测控制方法,以减少算法的计算量。
研究连续时间PWL系统的控制问题,提出了具有稳定性保证的混合预测控制器设计方法。首先,针对每一个子模态,分别设计有界控制器和预测控制器,并构造出连续时间PWL系统的稳定域估计集。然后,在稳定域估计集内,提出了一种基于预测控制和有界控制的混合控制切换策略,使得每个子模态在保证稳定性的同时,最优性也得到改善。在此基础上,利用多Lyapunov函数方法,保证了不同子模态之间切换的稳定性。该方法只需要针对每个子模态计算二次规划,不必对整个PWL系统求解定性和定量双重指标下的优化问题,降低了优化问题的计算复杂度。
网络控制系统是一类典型的具有混杂动态特性的系统,在运行的过程中不可避免地包含相互作用的离散和连续动态,因此,可以利用混杂动态系统控制理论和方法去解决网络控制系统中遇到的问题。采用多速率模式描述网络控制系统,可以减少由于网络拥塞而造成的信息丢失,得到更好的系统响应。针对输出采样周期是输入更新周期整数倍的多速率网络控制系统,将其建模为切换系统,给出了稳定性充分条件,并利用预测控制中的未来控制序列,对快速率控制律进行补偿,设计了依赖系统状态的能够镇定多速率网络控制系统的预测控制器。所提出的可镇定预测控制与传统的预测控制相比,可以有效地补偿网络诱导时滞对系统的影响。
网络带宽资源的限制,会产生网络诱导时滞、数据包丢失等问题,从而导致被控系统的性能降低甚至使系统失稳。为解决这一问题,一方面可以从系统设计的角度出发,对网络诱导时滞和丢包进行补偿。另一方面,可以从改善网络通讯性能出发,通过对网络通讯资源进行合理地分配和调度,降低网络带宽资源限制发生的可能性。从系统设计的角度出发,提出了一种多速率滚动时域状态估计器,以克服网络诱导时滞的影响,并对估计器的稳定性和无偏性进行了分析,给出当系统干扰有界情况下估计误差的上界。考虑到网络通讯约束对网络控制系统的影响,从改善网络通讯性能出发,通过引入逻辑变量组成的通讯调度矩阵,将多速率网络控制闭环系统建模为混合逻辑动态系统,提出了一种可镇定预测控制器设计方法。这种预测控制方法,在每个慢采样时刻,通过求解混合整数二次规划问题,得到一组稳定的快速率控制律,同时也得到了相应的网络调度策略。
Many complex processes not only include continuous physical, chemical and biologic reaction, but also are influenced by logic constraints, switching between different operating modes and human command, exhibiting hybrid dynamical characteristics. A class of complex systems in which continuous dynamic behavior and discrete dynamic behavior interact are called hybrid dynamical systems. The nonlinearity and even nonsmoothness of hybrid dynamical systems in nature make the problems of controller design and analysis very difficult, especially the case with constraints. Predictive control can deal with constraints, uncertainties and time delays. Also, it has the tolerance of model applied for prediction and efficiency of finite receding horizon optimization. Therefore, this methodology provides an important way for the control of hybrid dynamical systems. In this dissertation, predictive control is employed for hybrid dynamical systems, and the controller synthesis, the solution of optimization and the analysis of system performance are studied. The main contents are as follows.
Predictive controller design methods for discrete time piecewise linear (PWL) systems are studied in consideration of the modeling uncertainty and disturbances. For PWL systems with constraints and persistent, unknown but bounded disturbances, a constraints tightening robust predictive controller is presented. Based on optimization problem of predictive control for nominal PWL systems, the constraints are tightened to overcome the influence of persistent bounded disturbances. The proposed predictive controller can guarantee robust feasibility and convergence of closed-loop PWL systems, and reduce the complexity of computation. For uncertain structure of PWL systems that is described by a set of polytopic parameter varying models, an infinite horizon on-line predictive control technique for guaranteeing robust stability is developed by solving linear matrix matrices (LMIs). On the basis of the on-line algorithm, an improved algorithm is proposed to reduce computation.
For continuous-time PWL systems, a mixed predictive control strategy is proposed to guarantee global stability. For each mode of PWL systems, a bounded controller and a predictive controller are designed respectively, and a stable estimation region of PWL systems is developed. In the stable estimation region, a mixed control switching strategy based on predictive control and bounded control is given for each mode to achieve the reconciliation of stability and optimality properties. With the switching rules of different modes of PWL systems, the global stability can be guaranteed. In the proposed method, only quadratic programming problems are computed, which reduces on-line complexity of the optimization of hybrid dynamical systems.
As a class of hybrid dynamical systems, networked control systems (NCSs) include interacting discrete and continuous dynamical characteristics. Thus, hybrid systems control theory and approaches can be used in the control of NCSs. Using multirate scheme to describe NCSs can reduce the loss of information caused by network congestion, and can get a good response. For multirate networked control systems (MNCSs) with the output sampling period several times larger than the input updating period, we can use predictive control strategy to generate a set of future control sequences to compensate for the network-induced time delays. The closed-loop MNCSs are described as switched systems. Sufficient stability conditions are established via a switched Lyapunov function approach. Then, a predictive controller dependent on state for stabilizing MNCSs is proposed based on a finite input and state horizon cost with a finite terminal weighting matrix. Compared with traditional predictive control, the proposed stabilizing predictive control strategy can compensate for the influence of network-induced time delays.
Limited capacity for transmission of NCSs can lead to network-induced time delays, data losses and other problems, which can reduce systems performance and even destabilize systems. In order to overcome these problems, there are two approaches: (i) The influence of network-induced time delays and data packet loss can be compensated by system synthesis. (ii) The communication property can be improved by reasonable allocation and scheduling of network communication resources. From the perspective of systems synthesis, a receding horizon state estimation is proposed for MNCSs to overcome the influence of network-induced time delays. Convergence results and unbiasedness properties are analyzed. An upper bound of estimation error is presented under the assumption of bounded disturbances acting on the system and measurement equations. Taking the influence of communication constraints into account, from the perspective of improving communication performance, a communication scheduling matrix is introduced to describe possible scheduling, and the closed-loop MNCSs can be modeled as mixed logic dynamical systems. A predictive controller is designed by solving a mixed integer quadratic programming problem, which not only can stabilize closed-loop systems but also can present dynamical scheduling of communication channels.
引文
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