不确定切换系统的滑模控制方法研究
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摘要
切换系统是一类重要的混合动态系统,它由一组连续系统或者离散系统以及作用在其中的切换信号组成。在过去的二十年中,切换系统吸引了众多学者的关注,这主要是由于以下两个原因：第一,切换系统具有广泛的实际应用背景。在实际系统中,由于工作环境的突然变化、系统元部件磨损老化以及子系统内部联接的改变等因素会导致系统的结构发生突变,切换系统能有效的描述这类结构发生突变的系统；第二,切换系统的动态性能特殊复杂。切换信号的存在使得切换系统的稳定性分析特殊复杂,具体体现为切换系统的性质不是各个子系统性质的简单叠加,甚至可能会有截然不同的性质。
众所周知,滑模变结构控制具有快速响应、设计过程简单以及对参数不确定性和匹配干扰具有强鲁棒性等优良特性,因此,该方法自上世纪50年代被提出以来便成为了一种备受关注的鲁棒控制方法。近年来,伴随着切换系统的研究热潮,滑模控制方法开始被用于切换系统,并且已经取得了一些有意义的结果。然而值得注意的是,已有的工作都是在一些理想假设条件(输入通道相同、系统状态可测、控制元件正常工作以及数据完整传输)下展开讨论的,那么当上述假设条件不能满足时,研究和设计合适的滑模控制器对于提高切换系统的控制性能具有十分重要的理论价值和实际意义。
本文针对输入矩阵不同的切换系统,提出了输入矩阵加权方法,研究了系统在状态未知、控制器受限、执行器故障、观测器存在参数扰动以及信息非完整传输等复杂情况下切换系统的滑模控制问题,取得了一些有意义的研究成果。
本文主要工作包括：
(1)研究了一类不确定切换系统的滑模控制问题。针对输入矩阵不同的切换系统,提出了输入矩阵加权方法,构造了一个公共滑模面。设计了一个依赖于状态和时间的切换信号,运用多Lyapunov函数方法,讨论了滑动模态的渐近稳定性,并且设计滑模控制律保证了滑模面的可达性。在系统状态不可测的情况下,通过引入状态观测器,进一步考虑了切换系统的输出反馈控制问题；
(2)研究了执行器非线性受限情况下切换系统的滑模控制问题。首先运用上面提出的输入矩阵加权方法,构造了一个积分型公共滑模面。接着运用平均驻留时间方法,给出了滑动模态指数稳定性的充分条件。在控制输入包含扇区非线性和死区的情况下,设计了一种根据切换函数值的变化而采用不同形式的特殊的滑模控制器,可以保证滑模面的可达性；
(3)研究了执行器可能发生故障情况下切换系统的滑模可靠控制问题。首先建立了执行器故障模型,其中,各执行器通道均有可能发生不同程度的失效。基于被动可靠控制的思想,设计了一个鲁棒滑模控制器,在执行器故障、外界干扰以及不确定参数存在的情况下,证明了闭环系统的稳定性；
(4)研究了切换系统的自适应滑模可靠控制问题。通过在线估计执行器的失效程度,滑模控制器的参数得以在线更新,从而降低了单纯利用故障的上下界设计控制器带来的保守性,有效补偿了执行器故障给系统性能带来的影响,并设计依赖于平均驻留时间的切换信号,给出了滑动模态指数稳定的充分条件；
(5)研究了一类不确定切换系统的非脆弱滑模控制问题。构造一个状态观测器对不可测状态进行估计,其中,观测器增益可能发生参数摄动。设计了依赖于状态估计的非脆弱滑模控制器保证了滑模面的可达性。最后运用多Lyapunov函数方法,分析了滑动模态的指数稳定性；
(6)研究了系统状态信息可能发生丢包情况下离散切换系统的滑模控制问题。首先提出了一种补偿器弥补状态信息丢失,构造了一个依赖于丢包概率的公共滑模面。通过设计一个基于补偿器的滑模控制器,得到由状态变量和滑模变量组成的增广系统,利用随机稳定性理论,证明了在原点的状邻域内滑动模态均方指数稳定,并且系统状态轨迹于有限时间内被趋使到滑模面的带状邻域内。
As an important class of hybrid dynamical systems, switched systems are consisted of a series of continuous-time subsystems or discrete-time subsystems and a switching signal among them. In the past two decades, the stability analysis and stabilization of switched systems have received an increasing attention. The reasons can be seen in the following two aspects. Firstly, switched systems have been used widely in practice. In physical world, many plants may subejet to abrupt variations in their structures, due to sudden changes of the environment, system components aging and changing of subsystem's struture, which can be described as switched systems; Secondly, the dynamic analysis of switched systems is complex. Due to the existence of the switching signal, the sability analysis of switched systems is complex. A common example is that the dynamical performance of switched systems is not the simple superposition of the subsystems.
It is well known that, sliding mode control (SMC) has many desirable properties, such as fast response, simple design and strong robustness against both uncertain parameters and matched disturbances. Therefore, SMC strategy has been an important robust control method and attracted a lot of attentions since its appearance in the1950s. In recent years, SMC method has been used to analyze switched systems and many constructive results have been developed. However, it is worth noting that the aforementioned works were considered under the assumptions that the input channels were the same, the system state was available, the actuator or sensor worked normally, or the system signals could be successfully transmitted to the controller/actuator. Theorefore, when the above conditions are not satisfied, the sliding mode controller design of switched systems may have important theoretical and practical significance in developing control performance of switched systems.
For switched systems with different input matrices, a weighted sum of the input matrices is proposed. This thesis has discussed SMC of switched systems under the following cases: unavailable states, actuator nonlinearities, actuator faults, non-fragile observer and incomplete state information, and some meaningful results have been obtained.
The main contribution in this thesis is as follows:
(1) Considering the SMC for a calss of uncertain switched systems. Firstly, a weighted sum of the input matrices is proposed such that a common slidng surface is designed. Construct a switching signal depending on the state and time. Then, by employing the multiple Lyapunov function theory, the asymptotical stability of the sliding mode dynamics is analyzed. Moreover, a SMC law is designed to ensure the reachability of the sliding surface. Furthermore, when the system states are unmearable, by introducing a state observer, the output feedback control of switched systems is considered;
(2) Considering the problem of SMC for switched systems with actuator nonlinearities. Firstly, by means of the weighted sum approach, a common integral sliding surface is designed. And then, the efficient condition on the exponential stability of the sliding mode dynamics is geiven based on the average dwell time method. In the cases that the control input contains both sector nonlinearities and deadzones, a special sliding mode controller depending on the switched function is designed, by which the reachability of the specified sliding surface is guaranteed;
(3) Considering the reliable control of SMC for switched systems subject to actuator fualts. Firstly, the model of actuator faults with different degradation channels is proposed. And then, based on the theory of passive reliable control, a robust slidng mode controller is presented such that the closed-loop systems is exponentially stable despite the presence of actuator faults, external disturbances and uncertain parameters;
(4) Considering the adaptive sliding mode control of switched systems. By estimating the actuator failures online, the controller's parameters are updated adaptively. It not only reduce the conservatism compared with some existing approaches which only utilize the bound of the actuator gain variation, but also compensate effectively the effects of the gain variation of the actuators on the system performance. Finally, by designing a switching signal depending on the average dwell time, sufficient conditions on stability of the closed-loop systems were given;
(5) Considering the non-fragile control for switched systems with unmearable state. Firstly, to estimate the unmearable state, a state observer is introduced, in which the uncetrtain parameters exist. And then, an observer-based sliding mode controller is designed such that the reachability of the sliding surface can be ensured. Finally, by menas of the multiple Lyapunov function method, the exponential stability of the closed-loop systems is analyzed;
(6) Considering the SMC for discrete switched systems subject to incomplete state information. Firstly, a compensator is introduced such that the lost data can be estimated. A common sliding surface depending on the dropout-probability is constructed. And then, a compensator-dependent sliding mode law is designed. Thus, the augmented system consisted of system state and slidng variable is obtained. By employing the stochastic stability theory, it is shown that the sliding mode dynamics is mean square exponentially stable in a neighborhood of the origion. Meanwhile, the state trajectories are driven (with mean square) into a band of the sliding surface.
众所周知,滑模变结构控制具有快速响应、设计过程简单以及对参数不确定性和匹配干扰具有强鲁棒性等优良特性,因此,该方法自上世纪50年代被提出以来便成为了一种备受关注的鲁棒控制方法。近年来,伴随着切换系统的研究热潮,滑模控制方法开始被用于切换系统,并且已经取得了一些有意义的结果。然而值得注意的是,已有的工作都是在一些理想假设条件(输入通道相同、系统状态可测、控制元件正常工作以及数据完整传输)下展开讨论的,那么当上述假设条件不能满足时,研究和设计合适的滑模控制器对于提高切换系统的控制性能具有十分重要的理论价值和实际意义。
本文针对输入矩阵不同的切换系统,提出了输入矩阵加权方法,研究了系统在状态未知、控制器受限、执行器故障、观测器存在参数扰动以及信息非完整传输等复杂情况下切换系统的滑模控制问题,取得了一些有意义的研究成果。
本文主要工作包括：
(1)研究了一类不确定切换系统的滑模控制问题。针对输入矩阵不同的切换系统,提出了输入矩阵加权方法,构造了一个公共滑模面。设计了一个依赖于状态和时间的切换信号,运用多Lyapunov函数方法,讨论了滑动模态的渐近稳定性,并且设计滑模控制律保证了滑模面的可达性。在系统状态不可测的情况下,通过引入状态观测器,进一步考虑了切换系统的输出反馈控制问题；
(2)研究了执行器非线性受限情况下切换系统的滑模控制问题。首先运用上面提出的输入矩阵加权方法,构造了一个积分型公共滑模面。接着运用平均驻留时间方法,给出了滑动模态指数稳定性的充分条件。在控制输入包含扇区非线性和死区的情况下,设计了一种根据切换函数值的变化而采用不同形式的特殊的滑模控制器,可以保证滑模面的可达性；
(3)研究了执行器可能发生故障情况下切换系统的滑模可靠控制问题。首先建立了执行器故障模型,其中,各执行器通道均有可能发生不同程度的失效。基于被动可靠控制的思想,设计了一个鲁棒滑模控制器,在执行器故障、外界干扰以及不确定参数存在的情况下,证明了闭环系统的稳定性；
(4)研究了切换系统的自适应滑模可靠控制问题。通过在线估计执行器的失效程度,滑模控制器的参数得以在线更新,从而降低了单纯利用故障的上下界设计控制器带来的保守性,有效补偿了执行器故障给系统性能带来的影响,并设计依赖于平均驻留时间的切换信号,给出了滑动模态指数稳定的充分条件；
(5)研究了一类不确定切换系统的非脆弱滑模控制问题。构造一个状态观测器对不可测状态进行估计,其中,观测器增益可能发生参数摄动。设计了依赖于状态估计的非脆弱滑模控制器保证了滑模面的可达性。最后运用多Lyapunov函数方法,分析了滑动模态的指数稳定性；
(6)研究了系统状态信息可能发生丢包情况下离散切换系统的滑模控制问题。首先提出了一种补偿器弥补状态信息丢失,构造了一个依赖于丢包概率的公共滑模面。通过设计一个基于补偿器的滑模控制器,得到由状态变量和滑模变量组成的增广系统,利用随机稳定性理论,证明了在原点的状邻域内滑动模态均方指数稳定,并且系统状态轨迹于有限时间内被趋使到滑模面的带状邻域内。
As an important class of hybrid dynamical systems, switched systems are consisted of a series of continuous-time subsystems or discrete-time subsystems and a switching signal among them. In the past two decades, the stability analysis and stabilization of switched systems have received an increasing attention. The reasons can be seen in the following two aspects. Firstly, switched systems have been used widely in practice. In physical world, many plants may subejet to abrupt variations in their structures, due to sudden changes of the environment, system components aging and changing of subsystem's struture, which can be described as switched systems; Secondly, the dynamic analysis of switched systems is complex. Due to the existence of the switching signal, the sability analysis of switched systems is complex. A common example is that the dynamical performance of switched systems is not the simple superposition of the subsystems.
It is well known that, sliding mode control (SMC) has many desirable properties, such as fast response, simple design and strong robustness against both uncertain parameters and matched disturbances. Therefore, SMC strategy has been an important robust control method and attracted a lot of attentions since its appearance in the1950s. In recent years, SMC method has been used to analyze switched systems and many constructive results have been developed. However, it is worth noting that the aforementioned works were considered under the assumptions that the input channels were the same, the system state was available, the actuator or sensor worked normally, or the system signals could be successfully transmitted to the controller/actuator. Theorefore, when the above conditions are not satisfied, the sliding mode controller design of switched systems may have important theoretical and practical significance in developing control performance of switched systems.
For switched systems with different input matrices, a weighted sum of the input matrices is proposed. This thesis has discussed SMC of switched systems under the following cases: unavailable states, actuator nonlinearities, actuator faults, non-fragile observer and incomplete state information, and some meaningful results have been obtained.
The main contribution in this thesis is as follows:
(1) Considering the SMC for a calss of uncertain switched systems. Firstly, a weighted sum of the input matrices is proposed such that a common slidng surface is designed. Construct a switching signal depending on the state and time. Then, by employing the multiple Lyapunov function theory, the asymptotical stability of the sliding mode dynamics is analyzed. Moreover, a SMC law is designed to ensure the reachability of the sliding surface. Furthermore, when the system states are unmearable, by introducing a state observer, the output feedback control of switched systems is considered;
(2) Considering the problem of SMC for switched systems with actuator nonlinearities. Firstly, by means of the weighted sum approach, a common integral sliding surface is designed. And then, the efficient condition on the exponential stability of the sliding mode dynamics is geiven based on the average dwell time method. In the cases that the control input contains both sector nonlinearities and deadzones, a special sliding mode controller depending on the switched function is designed, by which the reachability of the specified sliding surface is guaranteed;
(3) Considering the reliable control of SMC for switched systems subject to actuator fualts. Firstly, the model of actuator faults with different degradation channels is proposed. And then, based on the theory of passive reliable control, a robust slidng mode controller is presented such that the closed-loop systems is exponentially stable despite the presence of actuator faults, external disturbances and uncertain parameters;
(4) Considering the adaptive sliding mode control of switched systems. By estimating the actuator failures online, the controller's parameters are updated adaptively. It not only reduce the conservatism compared with some existing approaches which only utilize the bound of the actuator gain variation, but also compensate effectively the effects of the gain variation of the actuators on the system performance. Finally, by designing a switching signal depending on the average dwell time, sufficient conditions on stability of the closed-loop systems were given;
(5) Considering the non-fragile control for switched systems with unmearable state. Firstly, to estimate the unmearable state, a state observer is introduced, in which the uncetrtain parameters exist. And then, an observer-based sliding mode controller is designed such that the reachability of the sliding surface can be ensured. Finally, by menas of the multiple Lyapunov function method, the exponential stability of the closed-loop systems is analyzed;
(6) Considering the SMC for discrete switched systems subject to incomplete state information. Firstly, a compensator is introduced such that the lost data can be estimated. A common sliding surface depending on the dropout-probability is constructed. And then, a compensator-dependent sliding mode law is designed. Thus, the augmented system consisted of system state and slidng variable is obtained. By employing the stochastic stability theory, it is shown that the sliding mode dynamics is mean square exponentially stable in a neighborhood of the origion. Meanwhile, the state trajectories are driven (with mean square) into a band of the sliding surface.
引文
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