状态估计与未知输入和可测噪声同时重构方法

针对一类不确定线性系统,讨论了状态估计及未知输入和可测噪声重构方法。首先,对仅具有未知输入的线性系统,讨论了观测器匹配条件不满足前提下的状态估计和未知输入重构问题;通过设计降维观测器和高阶滑模观测器,提出一种未知输入代数重构方法;然后,将以上结论上升到具有未知输入和可测噪声的线性系统,以此提出了状态估计及未知输入和可测噪声同时重构的方法;最后,通过对飞行器模型进行仿真,验证了所提出方法的有效性。     

基于辅助输出的线性系统状态和未知输入同时估计方法

在未知输入观测器匹配条件不满足的情况下, 针对一类线性时不变系统, 研究了同时估计系统 状态和未知输入的问题. 首先, 基于可测输出对未知输入的相关度的概念, 给出了辅助输出 的构造方法, 使得匹配条件得以满足. 为了处理辅助输出中的未知信息, 提出了一种高增益 观测器设计方法, 它不仅能估计辅助输出, 而且还能估计辅助输出的导数. 然后, 基于辅助 输出的估计值, 提出了一种降维观测器设计方法, 可以在不受未知输入影响的情况下估计系统 的状态; 接下来, 基于状态和辅助输出及其导数的估计值, 给出了未知输入估计. 最后, 对一个五 阶系统进行了数字仿真, 仿真结果表明所提出的方法是有效的.     

离散Lipschitz非线性系统状态和未知输入估计

针对含有未知输入和可测噪声的离散Lipschitz非线性系统,研究了状态估计、未知输入以及可测噪声同时估计的问题.首先,对含有未知输入的系统,设计了比例积分观测器,达到同时估计系统状态和未知输入之目的.分析了残差系统的观测性和稳定性,利用H_∞实现该观测器对时变未知输入的有效估计;其次,将观测器增益矩阵的求解转化为求解线性矩阵不等式的形式;进一步地,基于系统状态扩展方法,将所提方法推广至同时含有未知输入和可测噪声的系统;最后,通过两个仿真算例说明了所提方法的正确性和有效性.     

匹配条件不满足时线性系统未知输入观测器设计

针对一类不满足观测器匹配条件的线性系统,讨论了未知输入观测器设计方法.首先,为了突破观测器匹配条件的限制,提出了一种与未知输入相对阶无关的辅助输出构造方法.然后,把未知输入看作系统状态的一部分,将原系统转化为一个不含未知输入的增维线性描述系统.针对这样的系统转化,对一系列等价前提条件进行了详细的讨论.之后,针对该增维线性描述系统,构造Luenberger观测器来估计原系统的状态和未知输入.同时,借助于高阶滑模微分器,来估计辅助输出中的未知信号.最后,对一个单连杆柔性机械手模型进行了数值仿真,仿真结果表明了方法的有效性.     

不确定切换线性系统状态和未知输入估计方法

针对具有未知输入的不确定切换线性系统, 在平均驻留时间切换下, 讨论其状态和未知输入估计方法. 通过等价变换解耦切换系统的未知输入, 以构造降维切换系统. 进而, 设计切换观测器实现对原系统的状态估计, 并求解具有线性矩阵不等式限制的最优化问题, 得到观测器存在的充分条件. 在基于函数微分数值解方法求得系统输出微分的基础上, 提出一种切换系统未知输入的估计方法. 最后通过一个数值实例验证了所提出方法的有效性.

     

含未知输入的广义系统的状态与输入估计

研究了含未知输入的广义系统的输入解耦观测器设计问题. 在系统脉冲能控的条件下通过系统输入-状态对的非奇异变换, 把此问题等价地转化为正常状态空间系统的相应问题. 用大家熟知的方法设计正常状态空间系统的观测器, 从而得到广义系统的输入解耦观测器. 然后用广义系统的观测器状态和系统输出的线性组合渐近估计系统的状态与未知输入.     

基于高阶滑模观测器的状态和未知输入同时估计方法

对一类含有未知输入的仿射非线性系统,讨论了一种能同时估计系统状态和末知输入的未知输入观测器设计方法.首先利用李导数对仿射非线性系统进行线性化,将其转化为可控标准型.其次,针对变化后的等价系统,提出了一种高阶、高增益滑模观测器,由此不仅能得到系统状态的估计,同时还得到状态微分的估计.再次,基于状态及其微分的估计,对未知输入提出了一种重构方法.该方法能对强时变未知输入重构,而且重构中没有用到系统微分的信息.最后,通过对两个实际模型的仿真,表明了方法的可行性.     

切换系统激活模式辨识和有限时间状态估计北大核心CSCD

针对一类具有未知输入的不确定线性切换系统,考虑并利用有限时间观测器解决其激活模式辨识和有限时间状态估计问题。首先,利用状态和输出变换得到解耦未知输入的降维切换系统。其次,为每一个降维子系统设计一个对应的有限时间观测器,并对降维系统与观测器系统输出的残差范数进行最小化,从而提出一种激活模式辨识的方法。然后,通过有限时间观测器设置任意小的时间参数,实现了对降维解耦切换系统的有限时间状态估计,同时利用状态等价变化的方法得到原系统的有限时间状态估计。最后,通过MATLAB仿真验证了所提方法的可靠性。     

未知输入离散时滞奇异系统的观测器设计

讨论含未知输入的多时滞离散非方奇异系统的观测器设计问题．在两个一般秩的条件下，利用一系列等价变挟，将其转化为一个多时滞正常线性离散系统的观测器设计问题；利用线性矩阵不等式方法，给出了存在一个与系统状态维数相同的观测器的充分条件，并用此观测器对系统的状态和未知输入进行估计．     

非方广义系统的未知输入有限时间观测器设计

研究了含未知输入的非方广义系统的有限时间输入解耦观测器设计问题,在一定条件下基于非方广义系统的结构特征,引入一个输入-状态对的非奇异转换,把含未知输入的非方广义系统等价地转化为输入已知的正常状态空间系统．用传统的设计正常状态空间系统观测器的方法去构造含未知输入的非方广义系统的未知输入观测器,并给出了观测器存在的充分条件,由此得出了有限时间观测器的设计步骤．     

On Wonham stabilizability condition in the synthesis of observers for unknown-input systems

In this correspondence a stabilizability condition of Wonham is applied to the synthesis of dynamic observers for unknown-input linear multivariable systems. This approach leads to a stabilizability test of the observer structure considered, and may also lead to computerized design algorithms instead of actual tentative procedures.     

Design of unknown input functional observers for nonlinear systems with application to fault diagnosis

This paper considers the design of low-order unknown input functional observers for robust fault detection and isolation of a class of nonlinear Lipschitz systems subject to unknown inputs. The proposed functional observers can be used to generate residual signals to detect and isolate actuator faults. By using the generalized inverse approach, the effect of the unknown inputs can be decoupled completely from the residual signals. Conditions for the existence and stability of reduced-order unknown input functional observer are derived. A design procedure for the generation of residual signals to detect and isolate actuator faults is presented using the proposed unknown-input observer-based approach. A numerical example is given to illustrate the proposed fault diagnosis scheme in nonlinear systems subject to unknown inputs.     

Minimal unknown-input functional observers for multi-input multi-output LTI systems

Designing minimum possible order (minimal) disturbance-decoupled proper functional observers for multi-input multi-output (MIMO) linear time-invariant (LTI) systems is studied. It is not necessary that a minimum-order unknown-input functional observer (UIFO) exists in our proposed design procedure. If the minimum-order observer cannot be attained, the observer's order is increased sequentially through a recursive algorithm, so that the minimal order UIFO can be obtained. To the best of our knowledge, this is the first time that this specific problem is addressed. It is assumed that the system is unknown-input functional detectable, which is the least requirement for the existence of a stable UIFO. This condition also is a certificate for the convergence of our observer's order-increase algorithm. Two methodologies are demonstrated to solve the observer design equations. The second presented scheme, is a new design method that based on our observations has a better numerical performance than the first conventional one. Numerical examples and simulation results in the MATLAB/Simulink environment describe the overall observer design procedure, and highlight the efficacy of our new methodology to solve the observer equations in comparison to the conventional one.     

基于未知输入观测器的非线性时间序列故障预报

将未知非线性系统的输出作为时间序列并进行空间重构,针对得到的离散线性时变系统,提出了基于未知输入观测器的预测新方法.以实时拟合时间序列的线性AR模型作为时变系统的已知线性部分,将拟合误差作为时变系统的未知输入,实现了对非线性时间序列的一步预测.再利用递推预测的方法,将一步预测推广到N步预测,同时证明了该方法的预测误差有界.通过未知输入的预测值和状态的预测误差的变化可以方便地判断故障的发生,实现故障预报.仿真结果证明了方法的有效性.     

On geometric interpretation of extended state observer – A preliminary study

Borrowing the framework of the geometric approach, this paper tries to analyze and explain why it is possible for the extended state observer (ESO) to estimate the state vector and total disturbance accurately. The geometric approach has provided an elegant and rigorous framework to redefine some key concepts in modern control theory, such as controllability and observability. Moreover, those concepts can be extended to deal with systems in the presence of inaccessible disturbances, such as controlled invariants and conditioned invariants. It is shown in this paper that the augmented system of the ESO is unknown-state unknown-input completely reconstructable in finite time interval. A numerical simulation is given to verify the state vector and total disturbance can be estimated accurately by the ESO if the augmented system is unknown-state unknown-input completely reconstructable.     

Unknown-state, unknown-input reconstruction in discrete-time nonminimum-phase systems: Geometric methods

The complete solution to the unknown-state, unknown-input reconstruction problem in systems with invariant zeros is inherently conditioned by the fact that, for any invariant zero, at least one initial state exists, such that the output is not affected when the mode of the invariant zero is properly injected into the system. Despite this intrinsic limitation, the problem of reconstructing the initial state and the inaccessible inputs from the available measurements has recently attracted remarkable interest, owing to its impact on the synthesis of enhanced-reliability control systems. This contribution consists of a geometric method which solves the unknown-state, unknown-input reconstruction problem in discrete-time systems with invariant zeros anywhere in the complex plane, except the unit circumference. The case of systems with the invariant zeros in the open set outside the unit disc is regarded as the basic one. The difficulties related to the presence of those invariant zeros are overcome by accepting a reconstruction delay commensurate to the invariant zero time constants and the accuracy required for reconstruction. The solution devised for that case also applies to systems without invariant zeros. However, in this case, reconstruction is exact and the delay depends on the number of iterations needed for a certain conditioned invariant algorithm to converge. Finally, the more general case of systems with invariant zeros lying anywhere in the complex plane, with the sole exception of the unit circumference, is reduced to the fundamental one through the synthesis of an appropriate filter.     

Fuzzy observers for anaerobic WWTP: Development and implementation

In this paper a set of fuzzy observers for anaerobic digestion is proposed to estimate variables difficult to measure in a completely stirred tank reactor. First, a mathematical model for the process is stated and experimentally validated. Then, a methodology based on principal components analysis is developed to select fuzzy variables, which allow the local observers to be adequately activated. The active local observers are interpolated using the Takagi–Sugeno approach, in order to recover the non-linear behaviour; to ensure their adequate performance, the respective stability analysis is included. The whole estimation scheme is validated via simulations and tested in a real process.     

Uniformly Observable and Globally Lipschitzian Nonlinear Systems Admit Global Finite-Time Observers

There exist semi-global and finite-time converging observers for nonlinear systems that are uniformly observable and globally Lipschitzian. This was achieved with local finite-time stability theory, together with application of the technique of high-gain observers (the gain is constant). Under the same conditions, it is shown that these systems admit global finite-time observers. The proposed finite-time observers are based on a modified version of high-gain observer (now the gain is an exponential function with arbitrary growth rate). Design procedures are worked out for such observers, and a numerical example is presented to show the effectiveness of the proposed method.      

Nonlinear observer design for a general class of nonlinear systems with real parametric uncertainty

This paper is a geometric study of the local observer design for a general class of nonlinear systems with real parametric uncertainty. Explicitly, we study the observer design problem for a general class of nonlinear systems with real parametric uncertainty and with an input generator (exosystem). In this paper, we show that for the classical case, when the state equilibrium does not change with the parametric uncertainty, and when the plant output is purely a function of the state, there is no local asymptotic observer for the plant. Next, we show that in sharp contrast to this case, for the general case of problems where we allow the state equilibrium to change with the parametric uncertainty, there typically exist local exponential observers even when the plant output is purely a function of the state. We also present a characterization and construction procedure for local exponential observers for the general class of nonlinear systems with real parametric uncertainty under some stability assumptions. We also show that for the general class of nonlinear systems considered, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies, and is implied by, the existence of local exponential observers in the absence of inputs. Finally, we generalize our results to a general class of nonlinear systems with input generator, and with exogenous disturbance.