Distributed moving horizon state estimation for nonlinear systems with bounded uncertainties

In this work, we propose a distributed moving horizon state estimation (DMHE) design for a class of nonlinear systems with bounded output measurement noise and process disturbances. Specifically, we consider a class of nonlinear systems that are composed of several subsystems and the subsystems interact with each other via their subsystem states. First, a distributed estimation algorithm is designed which specifies the information exchange protocol between the subsystems and the implementation strategy of the DMHE. Subsequently, a local moving horizon estimation (MHE) scheme is designed for each subsystem. In the design of each subsystem MHE, an auxiliary nonlinear deterministic observer that can asymptotically track the corresponding nominal subsystem state when the subsystem interactions are absent is taken advantage of. For each subsystem, the nonlinear deterministic observer together with an error correction term is used to calculate a confidence region for the subsystem state every sampling time. Within the confidence region, the subsystem MHE is allowed to optimize its estimate. The proposed DMHE scheme is proved to give bounded estimation errors. It is also possible to tune the convergence rate of the state estimate given by the DMHE to the actual system state. The performance of the proposed DMHE is illustrated via the application to a reactor-separator process example.     

An interlaced extended Kalman filter

An estimation algorithm for a class of discrete time nonlinear systems is proposed. The system structure we deal with is partitionable into in subsystems, each affine w.r.t. the corresponding part of the state vector. The algorithm consists of a bank of m interlaced Kalman filters, and each of them estimates a part of the state, considering the remaining parts as known time-varying parameters whose values are evaluated by the other filters at the previous step. The procedure neglects the subsystem coupling terms in the covariance matrix of the state estimation error and counteracts the errors so introduced by suitably “increasing” the noise covariance matrices. Comparisons through numerical simulations with the extended Kalman filter and its modified versions proposed in the literature illustrate the good trade-off provided by the algorithm between the reduction of the computational load and the estimation accuracy     

基于降阶卡尔曼滤波器的水下机器人滑模容错控制

针对水下机器人执行器时变、非线性故障,提出一种基于降阶卡尔曼滤波器的故障估计和滑模容错控制方法.用降阶卡尔曼滤波器估计水下机器人故障解耦子系统的状态,受故障的影响,子系统状态可测.由估计的状态和测量的状态可进一步得到水下机器人执行器的故障信息.滑模容错控制器根据所估计的执行器故障调整控制器的输出以实现容错控制.仿真结果验证了所提出的故障辨识与容错控制算法的有效性.     

Distributed Fault Diagnosis With Overlapping Decompositions: An Adaptive Approximation Approach

This technical note deals with the problem of designing a distributed fault detection methodology for distributed (and possibly large-scale) nonlinear dynamical systems that are modelled as the interconnection of several subsystems. The subsystems are allowed to overlap, thus sharing some state components. For each subsystem, a local fault detector is designed, based on the measured local state of the subsystem as well as the transmitted variables of neighboring states that define the subsystem interconnections. The local detection decision is made on the basis of the knowledge of the local subsystem dynamic model and of an adaptive approximation of the interconnection with neighboring subsystems. The use of a specially-designed consensus-based estimator is proposed in order to improve the detectability of faults affecting variables shared among different subsystems. Simulation results provide an evidence of the effectiveness of the proposed distributed fault detection scheme.     

Extended Kalman filters for fractional‐order nonlinear continuous‐time systems containing unknown parameters with correlated colored noises

By using the Grünwald‐Letnikov (G‐L) difference method and the Tustin generating function method, this study presents extended Kalman filters to achieve satisfactory state estimation for fractional‐order nonlinear continuous‐time systems that containing some unknown parameters with the correlated fractional‐order colored noises. Based on the G‐L difference method and the Tustin generating function method, the difference equations corresponding to fractional‐order nonlinear continuous‐time systems are constructed respectively. The first‐order Taylor expansion is used to linearize the nonlinear functions in the estimated system, which provides the system model for extended Kalman filters. Using the augmented vector method, the unknown parameters are regarded as new state vectors, and the augmented difference equation is constructed. Based on the augmented difference equation, extended Kalman filters are designed to estimate the state of fractional‐order nonlinear systems with process noise as fractional‐order colored noise or measurement noise as fractional‐order colored noise. Meanwhile, the extended Kalman filters proposed in this paper can also estimate the unknown parameters effectively. Finally, the effectiveness of the proposed extended Kalman filters is validated in simulation with two examples.     

Observer-enhanced distributed moving horizon state estimation subject to communication delays

In this work, we focus on distributed moving horizon estimation (DMHE) of nonlinear systems subject to time-varying communication delays. In particular, a class of nonlinear systems composed of subsystems interacting with each other via their states is considered. In the proposed design, an observer-enhanced moving horizon state estimator (MHE) is designed for each subsystem. The distributed MHEs exchange information via a shared communication network. To handle communication delays, an open-loop state predictor is designed for each subsystem to provide predictions of unavailable subsystem states (due to delays). Based on the predictions, an auxiliary nonlinear observer is used to generate a reference subsystem state estimate for each subsystem. The reference subsystem state estimate is used to formulate a confidence region for the actual subsystem state. The MHE of a subsystem is only allowed to optimize its subsystem state estimate within the corresponding confidence region. Under the assumption that there is an upper bound on the time-varying delays, the proposed DMHE is proved to give decreasing and ultimately bounded estimation error. The theoretical results are illustrated via the application to a reactor–separator chemical process.     

Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises

In this paper, the problem of distributed weighted robust Kalman filter fusion is studied for a class of uncertain systems with autocorrelated and cross-correlated noises. The system under consideration is subject to stochastic uncertainties or multiplicative noises. The process noise is assumed to be one-step autocorrelated. For each subsystem, the measurement noise is one-step autocorrelated, and the process noise and the measurement noise are two-step cross-correlated. An optimal robust Kalman-type recursive filter is first designed for each subsystem. Then, based on the newly obtained optimal robust Kalman-type recursive filter, a distributed weighted robust Kalman filter fusion algorithm is derived for uncertain systems with multiple sensors. The distributed fusion algorithm involves a recursive computation of the filtering error cross-covariance matrix between any two subsystems. Compared with the centralized Kalman filter, the distributed weighted robust Kalman filter developed in this paper has stronger fault-tolerance ability. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.     

Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

In this paper, the adaptive control problem for a class of switched nontriangular nonlinear systems is investigated, which allows the control gains to vanish at some points. Neither the triangular structure nor the solvability of the adaptive control problem is required for each subsystem. A key point of this work is to solve the adaptive control problem of switched nontriangular nonlinear systems with vanishing control gains by the dual design of the controllers and switching signals. To this end, firstly, a hysteresis‐type control gains‐dependent switching law is designed, which makes the control gain of the active subsystem not vanish and thus the associated designed control input can enter into the active subsystem. Moreover, the designed switching law guarantees a dwell time between any adjacent switching instants, which rules out the Zeno behavior. Secondly, when the adaptive control problem of each subsystem is unsolvable, a sufficient condition ensuring the solvability of the adaptive control problem of switched nontriangular nonlinear systems is developed even if no control input can enter into subsystems at some points. Finally, the effectiveness of the proposed result is illustrated by two examples.     

Decentralized adaptive iterative learning control for interconnected systems with uncertainties

In many applications,the system dynamics allows the decomposition into lower dimensional subsystems with interconnections among them.This decomposition is motivated by the ease and flexibility of the controller design for each subsystem.In this paper,a decentralized model reference adaptive iterative learning control scheme is developed for interconnected systems with model uncertainties.The interconnections in the dynamic equations of each subsystem are considered with unknown boundaries.The proposed controller of each subsystem depends only on local state variables without any information exchange with other subsystems.The adaptive parameters are updated along iteration axis to compensate the interconnections among subsystems.It is shown that by using the proposed decentralized controller,the states of the subsystems can track the desired reference model states iteratively.Simulation results demonstrate that,utilizing the proposed adaptive controller,the tracking error for each subsystem converges along the iteration axis.     

分维自适应稀疏网格积分非线性滤波器

针对含加性高斯噪声的非线性离散系统,提出了可分别根据各维状态及量测方程的非线性函数特性来确定采样点及其权重的积分滤波器.设计了基于嵌入式高斯采样积分和稀疏网格法则的自适应多变量采样积分方法,可在匹配函数高阶泰勒展开项时,利用低阶采样点,提出了高效的数据结构和遍历算法,便于采用该积分方法分别估计系统状态/量测的预测均值和协方差矩阵.该滤波器既能根据各维非线性函数的特性确定采样点,又实现了对采样值和权重的完全复用,保证了算法效率.理论分析和仿真表明,该滤波算法中自适应调整的运算量小于计算非线性函数采样值.该滤波器与无迹卡尔曼滤波相比,提高了滤波精度,与固定形式的稀疏网格滤波器相比,提高了采样效率,且该方法为两者的广义形式.仿真实验也验证了状态估计的精确性和函数采样的高效性.     

Distributed sensor fault diagnosis in a class of interconnected nonlinear uncertain systems

In this paper, a distributed sensor fault detection and isolation (FDI) method is developed for a class of interconnected nonlinear uncertain systems. In the distributed FDI architecture, a FDI component is designed for each subsystem in the interconnected system. For each subsystem, its corresponding local FDI component is designed by utilizing local measurements and certain communicated information from neighboring FDI components associated with subsystems that are directly interconnected to the particular subsystem under consideration. Under certain assumptions, adaptive thresholds for distributed sensor fault detection and isolation in each subsystem are derived, ensuring robustness with respect to interactions among subsystems and system modeling uncertainty. Moreover, the fault detectability condition is rigorously investigated, characterizing the class of sensor faults in each subsystem that is detectable by the proposed distributed FDI method. Additionally, the stability and learning capability of the distributed adaptive fault isolation estimators is established. A simulation example of interconnected inverted pendulums mounted on carts is used to illustrate the effectiveness of the distributed FDI method.     

Decentralized filtering adaptive constrained tracking control for interconnected nonlinear systems

This paper presents a novel decentralized filtering adaptive constrained tracking control framework for uncertain interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, a piecewise constant adaptive law will generate total uncertainty estimates by solving the error dynamics between the host system and decentralized state predictor with the neglection of unknowns, whereas a decentralized filtering control law is designed to compensate both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. In the control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low‐pass filters, while the trade‐off between tracking and constraints violation avoidance is formulated as a numerical constrained optimization problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed‐loop reference system, which assumes partial cancelation of uncertainties within the bandwidth of the control signal. Compared with model predictive control (MPC) and unconstrained controller, the proposed control architecture is capable of solving the tracking control problems for interconnected nonlinear systems subject to constraints and uncertainties.     

State estimation of nonlinear dynamic systems using weighted variance-based adaptive particle swarm optimization

New heuristic filters are proposed for state estimation of nonlinear dynamic systems based on particle swarm optimization (PSO) and differential evolution (DE). The methodology converts state estimation problem into dynamic optimization to find the best estimate recursively. In the proposed strategy the particle number is adaptively set based on the weighted variance of the particles. To have a filter with minimal parameter settings, PSO with exponential distribution (PSO-E) is selected in conjunction with jDE to self-adapt the other control parameters. The performance of the proposed adaptive evolutionary algorithms i.e. adaptive PSO-E, adaptive DE and adaptive jDE is studied through a comparative study on a suite of well-known uni- and multi-modal benchmark functions. The results indicate an improved performance of the adaptive algorithms relative to original simple versions. Further, the performance of the proposed heuristic filters generally called adaptive particle swarm filters (APSF) or adaptive differential evolution filters (ADEF) are evaluated using different linear (nonlinear)/Gaussian (non-Gaussian) test systems. Comparison of the results to those of the extended Kalman filter, unscented Kalman filter, and particle filter indicate that the adopted strategy fulfills the essential requirements of accuracy for nonlinear state estimation.     

主–从滤波器设计及其在传递对准中的应用

本论文研究主一从自适应卡尔曼滤波器的设计及其在动基座传递对准中的应用．对于舰载惯性导航系统,利用速度加角速度匹配方案能够实现快速对准,然而该方案对船体挠曲变形比较敏感,若处理不当将造成对准精度下降．本文将挠曲变形视为对准过程中观测量的不确定性干扰噪声进行处理,并且利用方差匹配策略设计了主一从自适应滤波器,这两个滤波器并行运算,其中主滤波器用于估计惯性导航系统的状态,从滤波器用于估计噪声的统计特性．仿真结果表明,在对准模型存在未知的随机系统噪声时,所设计的滤波器能够快速且准确地估计出失准角,符合传递对准在快速性和精度方面的需求．     

确定采样型强跟踪滤波飞机舵面故障诊断与隔离

为了克服扩展多模型自适应估计中扩展卡尔曼滤波的理论局限性,多重渐消因子强跟踪改进引起的滤波发散现象以及多维高斯故障概率计算量大等问题,本文将一类基于确定解析采样近似方法的非线性次优高斯滤波与多模型自适应估计相结合,提出了改进的多重渐消因子强跟踪非线性滤波快速故障诊断方法.确定采样型滤波克服了扩展卡尔曼滤波的理论局限性;推导了等效多重渐消因子计算方法,避免了非线性系统雅克比矩阵的计算,提高了故障突变时的跟踪性能;提出了基于平方根分解的改进的一步预测协方差更新方程,保证了滤波稳定性;提出了基于欧几里得范数简化的故障概率计算方法,降低了计算量.通过对比仿真验证了3种不同非线性滤波算法及其强跟踪改进算法的有效性,故障诊断方法跟踪性强、速度快、精度高,具有较好的鲁棒性和稳定性.     

Decentralized event‐triggered control of large‐scale nonlinear systems

This paper studies the decentralized event‐triggered control of large‐scale nonlinear systems. We consider a class of decentralized control systems that are transformable into an interconnection of input‐to‐state stable subsystems with the sampling errors as the inputs. The sampling events for each subsystem are triggered by a threshold signal, and the threshold signals for the subsystems are independent with each other for the decentralized implementation. By appropriately designing the event‐triggering mechanisms, it is shown that infinitely fast sampling can be avoided for each subsystem and asymptotic regulation is achievable for the large‐scale system. The proposed design is based on the ISS small‐gain arguments, and is validated by a benchmark example of controlling two coupled inverted pendulums.     

Distributed fault diagnosis in a class of interconnected nonlinear uncertain systems

In this article, a distributed fault detection and isolation (FDI) method is developed for a class of interconnected nonlinear uncertain systems. In the distributed FDI architecture, a FDI component is designed for each subsystem in the interconnected system. For each subsystem, its corresponding local FDI component is designed by utilising local measurements and certain communicated information from neighbouring FDI components associated with subsystems that are directly interconnected to the particular subsystem under consideration. Under certain assumptions, adaptive thresholds for distributed FDI in each subsystem are derived, ensuring robustness with respect to interactions among subsystems and system modelling uncertainty. Moreover, the fault detectability and isolability conditions are rigorously investigated, characterising the class of faults in each subsystem that are detectable and isolable by the proposed distributed FDI method. Additionally, the stability and learning capability of the local adaptive fault isolation estimators designed for each subsystem is established. A simulation example of interconnected inverted pendulums mounted on carts is used to illustrate the effectiveness of the method.     

Continuous‐discrete filters for bearings‐only underwater target tracking problems

In this work, we develop a continuous‐discrete shifted Rayleigh filter (CD‐SRF) and a continuous‐discrete sparse‐grid Gauss‐Hermite filter (CD‐SGHF) for a real‐life passive underwater bearings‐only target tracking problem. The stochastic difference equation describing the process model is derived from its continuous equivalent using Ito‐Taylor expansion of order 1.5. The performance of the proposed filters is compared in terms of root mean square error (RMSE), track divergence and computational time. For a fair comparison, popular filters like the unscented Kalman filter (UKF), cubature Kalman filter (CKF) and Gauss–Hermite filter (GHF) are implemented. The effect of initial uncertainty, measurement noise covariance and sampling time on filtering accuracy is also studied. Finally, RMSEs of all the filters are evaluated in comparison with the Cramer–Rao lower bound (CRLB). From simulation results, it was observed that CD filters performed with higher accuracy than their discrete equivalents, with CD‐SRF proving to be the most accurate among all the filters.     

基于模糊卡尔曼滤波器的网络控制系统状态估计

针对基于T S模糊模型的网络控制系统提出了一种卡尔曼滤波器的设计方法．先运用卡尔曼滤波理论给每个子系统设计出子滤波器，然后通过这些子滤波器的模糊融合得出全局滤波器．本文证明此全局滤波器可实现无偏状态估计，并给出了其稳定的条件．最后用仿真实例验证了所提出的卡尔曼滤波器的有效性．     

Adaptive stabilization of nonlinear teleoperation systems: An SIIOS approach

In this paper, the adaptive control problem of nonlinear teleoperation system based on the point of view of state‐independent input‐to‐output stability is addressed. By intentionally introducing the switched filter systems, a new IOS‐based control framework based on subsystem decomposition is developed. By designing the proper nonlinear controller, the complete closed‐loop system is first modeled into two interconnected subsystems with some well‐defined auxiliary variables. Then utilizing the small gain theorem, the weakly state‐independent input‐to‐output stability of complete system can be derived by the stability of each subsystem. As an important extension, the proposed control scheme is also proved to be suitable for the control of the single‐master‐multi‐slave teleoperation systems. Finally, the numerical example is given to demonstrate the effectiveness. Copyright © 2016 John Wiley & Sons, Ltd.