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Stability analysis of jump-linear systems driven by finite-state machines with Markovian inputs.

机译：具有马尔可夫输入的有限状态机驱动的跳跃线性系统的稳定性分析。

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摘要

A control system with a fault recovery mechanism in the feedback loop and with faults occurring in a non-deterministic manner can be modeled as a class of hybrid systems, i.e., a dynamical system switched by a finite-state machine or an automaton. When the plant and controller are linear, such a system can be modeled as a jump-linear system driven by a finite-state machine with a random input process. Such fault recovery mechanisms are found in flight control systems and distributed control systems with communication networks. In these critical applications, closed-loop stability of the system in the presence of fault recoveries becomes an important issue.; Finite-state machines as mathematical constructs are widely used by computer scientists to model and analyze algorithms. In particular, fault recovery mechanisms that are implemented in hardware with logic based circuits and finite memory can be modeled appropriately with finite-state machines. In this thesis, mathematical tools are developed to determine the mean-square stability of a closed-loop system, modeled as a jump-linear system in series with a finite-state machine driven by a random process. The random input process is in general assumed to be any r-th order Markov process, where r ≥ 0. While stability tests for a jump-linear system with a Markovian switching rule are well known, the main contribution of the present work arises from the fact that output of a finite-state machine driven by a Markov process is in general not Markovian. Therefore, new stability analysis tools are provided for this class of systems and demonstrated through Monte Carlo simulations.
机译：可以将具有反馈回路中的故障恢复机制并且故障以不确定性方式发生的控制系统建模为一类混合系统，即由有限状态机或自动机切换的动态系统。当工厂和控制器为线性时，可以将这种系统建模为由有限状态机以随机输入过程驱动的跳跃线性系统。在具有通信网络的飞行控制系统和分布式控制系统中发现了这种故障恢复机制。在这些关键应用中，存在故障恢复的情况下系统的闭环稳定性成为重要问题。有限状态机作为数学构造物已被计算机科学家广泛用于建模和分析算法。特别是，可以使用有限状态机对在基于逻辑的电路和有限存储器的硬件​​中实现的故障恢复机制进行适当建模。在本文中，开发了数学工具来确定闭环系统的均方稳定性，将其建模为与由随机过程驱动的有限状态机串联的跳跃线性系统。一般将随机输入过程假定为任何r阶马尔可夫过程，其中r≥0。尽管具有马尔可夫切换规则的跳跃线性系统的稳定性测试是众所周知的，但本研究的主要贡献来自于由马尔可夫过程驱动的有限状态机的输出通常不是马尔可夫的事实。因此，为此类系统提供了新的稳定性分析工具，并通过蒙特卡洛模拟进行了演示。

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