非线性跳变系统的调度控制与故障检测
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摘要
大多数工程实际系统都会面临干扰以及环境变化等因素所带来的随机扰动，从而导致系统参数随机变化。Markov跳变系统的提出，对控制领域解决此类随机问题起到了极大的推动作用，该模型可以很好的描述实际中的网络系统，通信系统以及经济系统等等，Markov跳变系统的广泛应用，推动了学者们对其理论的研究和探索。另一方面，理想的线性系统是不存在的，自然界中的系统都是非线性的，随着工控规模的扩大，控制系统中的非线性特性越发明显，这导致了控制问题的复杂性。因此，研究非线性Markov跳变系统控制问题，是一个富有挑战性的课题，且理论和实践意义重大。
本文针对非线性Markov跳变系统，使用连续调度方法，分析了系统的随机稳定性，控制，滤波以及故障诊断等问题。本文的主要工作包括以下几个方面：
1）针对带有时滞的非线性Markov跳变系统，使用连续调度的方法，研究了其PI跟踪问题和滤波问题。同时，针对周期中立系统，将时间作为调度变量，实现了调度滤波，最终保证了滤波误差为零。
2）考虑到部分实际系统对状态轨迹暂态响应的要求，本文基于有限时间稳定理论，讨论了非线性Markov跳变系统的有限时间控制问题，并且设计了连续调度控制器，解决了状态可测以及不可测系统的有限时间控制问题。
3）当理论结果应用于实际时，我们遇到了执行器饱和这一限制因素。因此本文针对带有饱和输入的非线性Markov跳变系统，基于椭圆不变集理论，设计了连续调度控制器，最终，保证系统在输入非线性的情况下，系统是随机稳定的。
4）本文基于系统的解析模型，分别借助观测器和滤波器，研究了非线性Markov跳变系统的故障检测问题，设计了连续调度故障检测观测器和滤波器。该方法，保证了系统对故障的快速响应性能，同时也提高了系统对干扰的抑制作用。
5）由于实际中，存在一类符合非齐次跳变过程的随机系统，因此，本文应用多面体不变集，代替时变转移概率矩阵，结合凸集合的性质，分析了非线性非齐次Markov跳变系统的控制问题，实现了连续调度控制器的设计。
6）最后，给出了本论文的成果总结和对以后研究方向的展望，同时也指出了该方向亟待解决的问题。
In practice, many enginerring systems often exhibit random abrupt changes due to factors,such as environment changes or disturbances. These abrupt changing phenomena areobserved in many real practical systems, such as network systems, communication systems,and economic systems. They can be modelled as Markov jump systems. Furthermore, for areal practical problem, it is unrealistic to model it as a pure linear system because of factors,such as disturbances and possible input saturation. Thus, an accurate model of a real practicalcontrol problem tends to be complex and nonlinear. Therefore, the study of nonlinear Markovjump systems is both theoretically challenging and practically significant.
In this thesis, our concerns are on stability, control, filtering and fault detection problemsinvolving nonlinear Markov jump systems are being considered.The main contributions of the thesis are given below:
(i) PI tracking and filtering problems involving time delay nonlinear Markov jumpsystems are considered, using gain-scheduling approach. This tracking controller willensure the convergence of the tracking error. For cycle-neutral system, a filtering isrealised by taking the time as a scheduling variable such that the convergence of thefiltering error is achieved.
(ii) Finite time control problem, where the state of the nonlinear Markov jump systemis either measurable or unmeasurable. Based on the finite time stability theory, thegain scheduling approach is used to design controllers under which the closed-loopsystem is finite time stable.
(iii) In a real production process, each controller has its own working limitation. Here,we introduce input saturation into the nonlinear Markov jump system. Then, by virtueof the ellipsoid invariant set, a continuous scheduling control is designed under whichthe closed-loop system is stable.
(iv) Based on the system model, fault detection observer and filtering are used torealize the fault detection problem for nonlinear Markov jump systems. Then, thegain-scheduled fault detection observer and filter are designed under which both therobustness and sensitivities are guaranteed.
(v) By using the polyhedral set to characterize the time-varying transition probabilities,a continuous gain-scheduled controller is designed for the non-homogeneousnonlinear Markov jump system. Our simulation results show that the proposedapproach is effective.
(vi) Finally, we give a summary of the thesis and make some suggestions for futureresearch directions of the area. Some interesting problems, which are yet to besolved, are also given.
本文针对非线性Markov跳变系统，使用连续调度方法，分析了系统的随机稳定性，控制，滤波以及故障诊断等问题。本文的主要工作包括以下几个方面：
1）针对带有时滞的非线性Markov跳变系统，使用连续调度的方法，研究了其PI跟踪问题和滤波问题。同时，针对周期中立系统，将时间作为调度变量，实现了调度滤波，最终保证了滤波误差为零。
2）考虑到部分实际系统对状态轨迹暂态响应的要求，本文基于有限时间稳定理论，讨论了非线性Markov跳变系统的有限时间控制问题，并且设计了连续调度控制器，解决了状态可测以及不可测系统的有限时间控制问题。
3）当理论结果应用于实际时，我们遇到了执行器饱和这一限制因素。因此本文针对带有饱和输入的非线性Markov跳变系统，基于椭圆不变集理论，设计了连续调度控制器，最终，保证系统在输入非线性的情况下，系统是随机稳定的。
4）本文基于系统的解析模型，分别借助观测器和滤波器，研究了非线性Markov跳变系统的故障检测问题，设计了连续调度故障检测观测器和滤波器。该方法，保证了系统对故障的快速响应性能，同时也提高了系统对干扰的抑制作用。
5）由于实际中，存在一类符合非齐次跳变过程的随机系统，因此，本文应用多面体不变集，代替时变转移概率矩阵，结合凸集合的性质，分析了非线性非齐次Markov跳变系统的控制问题，实现了连续调度控制器的设计。
6）最后，给出了本论文的成果总结和对以后研究方向的展望，同时也指出了该方向亟待解决的问题。
In practice, many enginerring systems often exhibit random abrupt changes due to factors,such as environment changes or disturbances. These abrupt changing phenomena areobserved in many real practical systems, such as network systems, communication systems,and economic systems. They can be modelled as Markov jump systems. Furthermore, for areal practical problem, it is unrealistic to model it as a pure linear system because of factors,such as disturbances and possible input saturation. Thus, an accurate model of a real practicalcontrol problem tends to be complex and nonlinear. Therefore, the study of nonlinear Markovjump systems is both theoretically challenging and practically significant.
In this thesis, our concerns are on stability, control, filtering and fault detection problemsinvolving nonlinear Markov jump systems are being considered.The main contributions of the thesis are given below:
(i) PI tracking and filtering problems involving time delay nonlinear Markov jumpsystems are considered, using gain-scheduling approach. This tracking controller willensure the convergence of the tracking error. For cycle-neutral system, a filtering isrealised by taking the time as a scheduling variable such that the convergence of thefiltering error is achieved.
(ii) Finite time control problem, where the state of the nonlinear Markov jump systemis either measurable or unmeasurable. Based on the finite time stability theory, thegain scheduling approach is used to design controllers under which the closed-loopsystem is finite time stable.
(iii) In a real production process, each controller has its own working limitation. Here,we introduce input saturation into the nonlinear Markov jump system. Then, by virtueof the ellipsoid invariant set, a continuous scheduling control is designed under whichthe closed-loop system is stable.
(iv) Based on the system model, fault detection observer and filtering are used torealize the fault detection problem for nonlinear Markov jump systems. Then, thegain-scheduled fault detection observer and filter are designed under which both therobustness and sensitivities are guaranteed.
(v) By using the polyhedral set to characterize the time-varying transition probabilities,a continuous gain-scheduled controller is designed for the non-homogeneousnonlinear Markov jump system. Our simulation results show that the proposedapproach is effective.
(vi) Finally, we give a summary of the thesis and make some suggestions for futureresearch directions of the area. Some interesting problems, which are yet to besolved, are also given.
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