Efficient routing redundancy design over lossy networks

In this paper, a wireless networked control system is made robust with respect to packet losses by exploiting routing redundancy. Multiple copies of sensing and actuation data are sent via different routing paths, associated to possibly different delays. Similar to linear network coding, such data are recombined as a weighted linear combination. A MIMO output‐feedback architecture is considered. A methodology that takes into account both the network parameters and the plant dynamics is proposed to set up an optimization problem to design network weights to satisfy a robustness metric based on the notion of asymptotic mean‐square stability. Such metric induces either an objective or a constraint function that is nonlinear. For this reason, an efficient suboptimal design methodology is also proposed. Finally, the solutions are compared with the optimal choice from the communication designer point of view, which is based on the minimization of the quadratic error induced by the network on the actuation signal. The suboptimal methodology is shown, by means of a nontrivial example, to give results extremely close to the optimum with a strongly reduced computation time. It is also shown that the optimal choice from the communication design point of view, which neglects the plant dynamics, does not guarantee stochastic stability.     

一种考虑先验估计误差相关性的快速DUIF 算法

针对稀疏无线传感器网络(WSN) 中加权平均一致分布式无迹信息滤波(DUIF) 算法估计次优和滤波效率较低的问题, 提出一种考虑先验估计误差相关性的快速DUIF 算法. 采用加权统计线性回归(WSLR) 方法线性化观测模型, 以节点共享信息作为平均一致性算法输入, 从而在极大后验估计中引入先验估计交互协方差信息; 设计最优通信连接边权值并自适应修正状态加权矩阵, 提高平均一致性算法收敛速率. 仿真实验结果表明, 所提出的算法能够有效应用于稀疏WSN目标跟踪.

     

Adaptive composite suboptimal control for linear singularly perturbed systems with unknown slow dynamics

In this article, using singular perturbation theory and adaptive dynamic programming (ADP) approach, an adaptive composite suboptimal control method is proposed for linear singularly perturbed systems (SPSs) with unknown slow dynamics. First, the system is decomposed into fast‐ and slow‐subsystems and the original optimal control problem is reduced to two subproblems in different time‐scales. Afterward, the fast subproblem is solved based on the known model of the fast‐subsystem and a fast optimal control law is designed by solving the algebraic Riccati equation corresponding to the fast‐subsystem. Then, the slow subproblem is reformulated by introducing a system transformation for the slow‐subsystem. An online learning algorithm is proposed to design a slow optimal control law by using the information of the original system state in the framework of ADP. As a result, the obtained fast and slow optimal control laws constitute the adaptive composite suboptimal control law for the original SPSs. Furthermore, convergence of the learning algorithm, suboptimality of the adaptive composite suboptimal control law and stability of the whole closed‐loop system are analyzed by singular perturbation theory. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed methods.     

A New Poisson Noise Filter Based on Weights Optimization

We propose a new image denoising algorithm when the data is contaminated by a Poisson noise. As in the Non-Local Means filter, the proposed algorithm is based on a weighted linear combination of the observed image. But in contrast to the latter where the weights are defined by a Gaussian kernel, we propose to choose them in an optimal way. First some “oracle” weights are defined by minimizing a very tight upper bound of the Mean Square Error. For a practical application the weights are estimated from the observed image. We prove that the proposed filter converges at the usual optimal rate to the true image. Simulation results are presented to compare the performance of the presented filter with conventional filtering methods.     

Linear estimation for random delay systems

This paper is concerned with the linear estimation problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time-stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal linear filter is presented based on the Kalman filtering technique. However, the optimal filter is time-varying, stochastic, and does not converge to a steady state in general. Then an alternative suboptimal filter with deterministic gains is developed under a new criteria. The estimator performance in terms of their error covariances is provided, and its mean square stability is established. Finally, a numerical example is presented to illustrate the efficiency of proposed estimators.     

Optimal structure of continuous nonlinear reduced-order Pugachev filter

A non-parametric synthesis problem is considered for a fast nonlinear low-memory filter consisting of the same number of equations as the number of only information components of the diffusion Markovian state vector of the observation plant. The algorithm for finding mean-square locally optimal structural functions of the filter and the reduced Fokker-Planck-Kolmogorov equation to be used to find the respective instantaneously conditional probability distribution are obtained. The proposed filter in its full order is proved to coincide with the linear Kalman-Bucy filter in various linear Gaussian cases. Ways to construct Gaussian and linearized suboptimal filters are proposed. The example is given where the latter are compared with their analogues.     

On the optimality of two‐stage Kalman filtering for systems with unknown inputs

This paper is concerned with the optimal solution of two‐stage Kalman filtering for linear discrete‐time stochastic time‐varying systems with unknown inputs affecting both the system state and the outputs. By means of a newly‐presented modified unbiased minimum‐variance filter (MUMVF), which appears to be the optimal solution to the addressed problem, the optimality of two‐stage Kalman filtering for systems with unknown inputs is defined and explored. Two extended versions of the previously proposed robust two‐stage Kalman filter (RTSKF), augmented‐unknown‐input RTSKF (ARTSKF) and decoupled‐unknown‐input RTSKF (DRTSKF), are presented to solve the general unknown input filtering problem. It is shown that under less restricted conditions, the proposed ARTSKF and DRTSKF are equivalent to the corresponding MUMVFs. An example is given to illustrate the usefulness of the proposed results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

State waypoint approach to continuous‐time nonlinear optimal control problems

In this paper, we propose an optimal control technique for a class of continuous‐time nonlinear systems. The key idea of the proposed approach is to parametrize continuous state trajectories by sequences of a finite number of intermediate target states; namely, waypoint sequences. It is shown that the optimal control problem for transferring the state from one waypoint to the next is given an explicit‐form suboptimal solution, by means of linear approximation. Thus the original continuous‐time nonlinear control problem reduces to a finite‐dimensional optimization problem of waypoint sequences. Any efficient numerical optimization method, such as the interior‐reflection Newton method, can be applied to solve this optimization problem. Finally, we solve the optimal control problem for a simple nonlinear system example to illustrate the effectiveness of this approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Networked LQG control over unreliable channels

In this article, the linear quadratic Gaussian (LQG) optimal control problem for networked control systems when data is transmitted through a transmission control protocol (TCP)‐like network and both measurement and control packets are subject to random packet dropouts, is addressed for two cases. In the ?rst case, it is assumed that the control acknowledgment packets in TCP‐like protocols are always available, that is, they always reach the ?lter‐controller unit on time and without fail, and we propose how to design a linear optimal ‘hold‐input’ control law for this case. In the second problem, we assume the acknowledgement packets may go missing with a known probability. This case is known to be di?cult and the optimal control law would be nonlinear. Hence, we derive a suboptimal linear estimation‐control law instead. Simulation results are presented to demonstrate the effectiveness of the proposed approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

多传感器最优信息融合白噪声反卷积滤波器

应用现代时间序列分析方法和白噪声估计理论,基于线性最小方差意义下按标量加权最优信息融合准则,对于带白色和有色观测噪声的多传感器单通道系统,提出了分布式融合白噪声反卷积滤波器.它由局部白噪声反卷积滤波器加权构成.可统一处理融合滤波、平滑和预报问题.给出了计算局部滤波误差互协方差公式,可用于计算最优加权.同单传感器情形相比,可提高融合滤波器精度.它可应用于石油地震勘探信号处理.一个3传感器信息融合Bernou lli-Gaussian白噪声反卷积滤波器的仿真例子说明了其有效性.     

Optimal sequential and distributed fusion for state estimation in cross-correlated noise

This paper is concerned with the optimal state estimation for linear systems when the noises of different sensors are cross-correlated and also coupled with the system noise of the previous step. We derive the optimal linear estimation in a sequential form and for distributed fusion. They are both compared with the optimal batch fusion, suboptimal batch fusion, suboptimal sequential fusion, and the suboptimal distributed fusion where the cross-correlation between the noises are neglected. The comparison is in terms of theoretical filter mean square error and the real root mean square error. Simulation on a target tracking example is given to show the effectiveness of the presented algorithms.     

Multi-sensor information fusion white noise filter weighted by scalars based on Kalman predictor

A unified multi-sensor optimal information fusion criterion weighted by scalars is presented in the linear minimum variance sense. The criterion considers the correlation among local estimation errors, only requires the computation of scalar weights, and avoids the computation of matrix weights so that the computational burden can obviously be reduced. Based on this fusion criterion and Kalman predictor, an optimal information fusion filter for the input white noise, which can be applied to seismic data processing in oil exploration, is given for discrete time-varying linear stochastic control systems measured by multiple sensors with correlated noises. It has a two-layer fusion structure. The first fusion layer has a netted parallel structure to determine the first-step prediction error cross-covariance for the state and the filtering error cross-covariance for the input white noise between any two sensors at each time step. The second fusion layer is the fusion center to determine the optimal scalar weights and obtain the optimal fusion filter for the input white noise. Two simulation examples for Bernoulli-Gaussian white noise filter show the effectiveness.     

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.     

Infinite horizon optimal control for nonlinear interconnected large‐scale dynamical systems with an application to optimal attitude control

This paper presents a novel extended modal series method for solving the infinite horizon optimal control problem of nonlinear interconnected large‐scale dynamic systems. In this method, the infinite horizon nonlinear large‐scale two‐point boundary value problem (TPBVP), derived from Pontryagin's maximum principle, is transformed into a sequence of linear time‐invariant TPBVPs. Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of a uniformly convergent series. Moreover, in special cases, the proposed procedure facilitates the application of parallel processing, which improves its computational efficiency. In this study, an iterative algorithm is also presented, which has a low computational complexity and a fast convergence rate. Just a few iterations are required to obtain a suboptimal trajectory‐control pair. Finally, effectiveness of the proposed approach is verified by solving the optimal attitude control problem. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Jump linear quadratic Gaussian control in continuous time

The optimal quadratic control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes is addressed. The systems are also subject to Gaussian input and measurement noise. The optimal solution for the jump linear-quadratic-Gaussian (JLQC) problem is given. This solution is based on a separation theorem. The optimal state estimator is sample-path dependent. If the plant parameters are constant in each value of the underlying jumping process, then the controller portion of the compensator converges to a time-invariant control law. However, the filter portion of the optimal infinite time horizon JLQC compensator is not time invariant. Thus, a suboptimal filter which does converge to a steady-state solution (under certain conditions) is derived, and a time-invariant compensator is obtained     

Multi-sensor optimal information fusion Kalman filter

This paper presents a new multi-sensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, it is equivalent to the maximum likelihood fusion criterion under the assumption of normal distribution. Based on this optimal fusion criterion, a general multi-sensor optimal information fusion decentralized Kalman filter with a two-layer fusion structure is given for discrete time linear stochastic control systems with multiple sensors and correlated noises. The first fusion layer has a netted parallel structure to determine the cross covariance between every pair of faultless sensors at each time step. The second fusion layer is the fusion center that determines the optimal fusion matrix weights and obtains the optimal fusion filter. Comparing it with the centralized filter, the result shows that the computational burden is reduced, and the precision of the fusion filter is lower than that of the centralized filter when all sensors are faultless, but the fusion filter has fault tolerance and robustness properties when some sensors are faulty. Further, the precision of the fusion filter is higher than that of each local filter. Applying it to a radar tracking system with three sensors demonstrates its effectiveness.     

Distributed Filtering for Multi-sensor Systems with Missing Data

This paper studies distributed estimation problems for multi-sensor systems with missing data. Missing data may occur during sensor measuring or data exchanging among sensor nodes due to unreliability of communication links or external disturbances. Missing data include random missing measurements of sensor itself and random missing estimates of neighbor nodes. Three distributed Kalman filter (DKF) algorithms with the Kalman-like form are designed for each sensor node. When it is available whether a datum is missing or not at each time, an optimal DKF (ODKF) dependent on the knowledge of missing data is presented, where filter gains and covariance matrices require online computing. To reduce online computational cost, a suboptimal DKF (SDKF) is presented, where filter gains and covariance matrices dependent on missing probabilities can be computed offline. When it is unavailable whether a datum is missing or not, a probability-based DKF (PDKF) dependent on missing probabilities is presented. For each DKF algorithm, an optimal Kalman filter gain for measurements of sensor itself and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense, respectively. Mean boundedness of covariance matrix of the proposed ODKF is analyzed. Stability and steady-state properties of the proposed SDKF and PDKF are analyzed. Also, the performance of three DKF algorithms is compared. Simulation examples demonstrate effectiveness of the proposed algorithms.     

Decoupling Controller with Disturbance Observer for LTI MIMO Systems

In this paper, a decoupling multivariable control strategy for linear time‐invariant (LTI) multi‐input/multi‐output (MIMO) systems is proposed. The strategy includes a multivariable disturbance observer (MDOB) and a decoupling controller. This MDOB is introduced to improve the system performances when the system encounters severe external disturbances. H₂ optimal scheme is utilized to design the MDOB filter. The controller is developed based on an inverse control method, through which the design process can be simplified. Simulation results certify the effectiveness of the proposed control strategy.     

Modeling and estimation for networked systems with multiple random transmission delays and packet losses

In networked systems, data packets are transmitted through networks from a sensor to a data processing center. Due to the unreliability of communication channels, a packet may be delayed even lost during the transmission. At each moment, the data processing center may receive one or multiple data packets or nothing at all. A novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of Bernoulli distributed random variables. It is transformed to a measurement model with multiple random delayed states and noises. Based on the model, an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate. It does not have a steady-state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment. So it needs to be computed online. To reduce the online computational cost, a suboptimal linear filter dependent on the probabilities of random variables is also proposed. However, it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities. It can be computed offline since it has the steady-state performance. A sufficient condition of existence for the steady-state performance is given. A simulation example shows the effectiveness.     

Smoothing properties of discrete-time zero-lag Kalman filter

In this paper it is shown than an estimate generated in a discrete time Kalman filter can, under certain circumstances, give better performance if some delay is allowed in the system. This fact is utilized to construct three simple suboptimal smoothers, all based on the structure of a Kalman filter. These smoothers are of low complexity as compared with the optimal ones. The conditions are given under which the performance of these suboptimal smoothers is better than that of a zero-lag Kalman filter. The methods of suboptimal smoothing considered give, in many cases, a possibility of obtaining results close to the optimal smoother. Several examples are presented.