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This paper studies consensus problems of multi-agent systems with binary-valued communications. Different from most existing works, the agents considered in this paper can only get binary-valued observations of its neighbors’ states with random noises. A consensus algorithm is proposed: first, each agent estimates its neighbors’ states by the recursive projection algorithm; then, each agent designs the control timely based on the estimates. It is proved that the estimates of the states can converge to the true states with a faster convergence rate than that in the parameter estimation. Moreover, the states of the agents can achieve mean-square consensus, and the corresponding consensus speed can achieve $O(1/t)$ under certain conditions. Finally, simulations are given to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a bound-based simulation budget allocation (BSBA) procedure for solving ranking and selection (R&S) problems in simulation optimization. For many practical applications, strict bounds on system performances can be obtained through empirical and theoretical approaches. These bounds provide additional information which may help solve R&S problems. In this paper, a new method of objective function estimation is proposed using both bound information and simulation outputs. This new estimation method is demonstrated to be particularly effective. To solve R&S problems, several asymptotic optimal allocation rules are also derived. Using these allocation rules, a BSBA procedure is proposed to achieve high efficiency in identifying the best design. Numerical experiments are provided to examine the performance of the proposed BSBA procedure. The computational results show that BSBA outperforms three compared allocation procedures, especially when bounds are tight or the simulation budget is small. [ABSTRACT FROM AUTHOR]

This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min–max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush–Kuhn–Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a suitable feasible set. Two distributed algorithms are considered, based on projections of the estimate of each agent onto its local feasible set. The main contribution of the paper is to show that such algorithms are asymptotic interpolatory estimators, i.e., they converge to an element of the global feasible set, under the assumption that the feasible set associated to each measurement is convex. The proposed techniques are demonstrated on a distributed linear regression estimation problem. [ABSTRACT FROM AUTHOR]

In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback–Leibler approximation of spectral densities, proposed by Pavon and Ferrante in their paper “On the Georgiou–Lindquist approach to constrained Kullback–Leibler approximation of spectral densities.” Our main result states that the algorithm globally converges to one of its fixed points. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of continuous-time nonlinear filtering of stochastic processes evolving on connected Riemannian manifolds without boundary. The main contribution of this paper is to derive the feedback particle filter (FPF) algorithm for this problem. In its general form, the FPF is shown to provide an intrinsic description of the filter that automatically satisfies the geometric constraints of the manifold. The particle dynamics are encapsulated in a Stratonovich stochastic differential equation that retains the feedback structure of the original (Euclidean) FPF. The implementation of the filter requires a solution of a Poisson equation on the manifold, and a numerical algorithm is described for this purpose. For the special case when the manifold is a matrix Lie group, explicit formulae for the filter are derived, using the matrix coordinates. Filters for two example problems are presented: the attitude estimation problem on $SO(3)$ and the robot localization problem in $SE(3)$. Comparisons are also provided between the FPF and popular algorithms for attitude estimation, namely the multiplicative extended Kalman filter (EKF), the invariant EKF, the unscented quaternion estimator, the invariant ensemble Kalman filter, and the bootstrap particle filter. Numerical simulations are presented to illustrate these comparisons. [ABSTRACT FROM AUTHOR]

In this paper, the problem of estimation is considered for a class of processes involving solidifying materials. These processes have natural nonlinear infinite-dimensional representations, and measurements are only available at particular points in the caster, each corresponding to a single discrete-in-time boundary measurement in the Stefan problem partial differential equation (PDE) mathematical model. The results for two previous estimators are summarized. The first estimator is based on the Stefan problem, using continuous instead of discrete-in-time boundary measurements. The second estimator employs a process model that is more detailed than the Stefan problem, but with no output injection to reduce estimation error, other than model calibration. Both of these estimation frameworks are extended in the current paper to a more realistic sensing setting. First, an estimator is considered that uses the Stefan problem under some simplifying but practically justified assumptions on the unknowns in the process. The maximum principle for parabolic PDEs is employed to prove that online calibration using a single discrete-in-time temperature measurement can provide removal of the estimation error arising due to mismatch of a single unknown parameter in the model. Although unproven, this result is then shown in simulation to apply to the more detailed process model. [ABSTRACT FROM PUBLISHER]

This article considers a nonlinear filtering method for handling outliers. The presence of outliers that are gross observation errors can greatly reduce the accuracy of filtering methods that assume Gaussian distributed errors. There are some existing methods that assume a Gaussian observation error, and estimate the error covariance matrix at each time step to avoid overfitting to the outliers. However, the estimates of the covariance matrix under such methods can become unstable. This results in underfitting or overfitting to observations when filtering. This paper presents a new method for handling outliers in nonlinear filtering problems by extending the unscented Kalman filter. In this method, two Gaussian observation error models with distinct covariance matrices are used: one for observations with regular errors, and another with a larger variance specified by a scale parameter for outliers. In addition to the system state, this method estimates an indicator variable that switches between the two models and the scale parameter for outliers. With the inclusion of the indicator variable and scale parameter, the estimated error covariance matrix can handle both regular observations and outliers appropriately at each time step. Furthermore, by estimating the scale parameter, the proposed method can be applied to a dataset without additional tuning to account for outlier characteristics. Through numerical experiments, we find that our method can estimate the system state better than existing methods for both datasets with and without outliers. [ABSTRACT FROM AUTHOR]

The paper extends a recently proposed indirect, certainty-equivalence, event-triggered adaptive control scheme to the case of nonobservable parameters. The extension is achieved by using a novel batch least-squares identifier (BaLSI), which is activated at the time of the events. BaLSI guarantees the finite-time asymptotic constancy of the parameter estimates and the fact that the trajectories of the closed-loop system follow the trajectories of the nominal closed-loop system (nominal in the sense of the asymptotic parameter estimate, not in the sense of the true unknown parameter). Thus, if the nominal feedback guarantees global asymptotic stability and local exponential stability, then unlike conventional adaptive control, the newly proposed event-triggered adaptive scheme guarantees global asymptotic regulation with a uniform exponential convergence rate. The developed adaptive scheme is tested to a well known control problem—the state regulation of the wing-rock model. Comparisons with other adaptive schemes are also provided for this particular problem. [ABSTRACT FROM AUTHOR]

In this paper, we focus on extended Kalman filtering (EKF), in the difficult case where a function of the state has been perfectly observed, and is thus known with certainty, while the full state still has unobserved degrees of freedom. In the linear case, the Kalman filter seamlessly handles such constraints, which result in the state being in an affine subspace. Yet, in the nonlinear case, the EKF poorly handles such type of constraints. As a remedy, we propose a novel general methodology of EKF based on an (arbitrary) nonlinear error $e$. And we prove that under compatibility of the error $e$ with the constraints, the EKF based on $e$ seamlessly handles the constraints. Furthermore, when the state space is a Lie group, we prove the EKF based on invariant errors is exactly the invariant EKF (IEKF), and we prove further properties. The theory is applied to the problem of simultaneous localization and mapping, where the IEKF is shown to perfectly handle some partial deterministic information about the map. As a byproduct, the theory is also shown to readily allow devising EKFs on state spaces defined by a class of equality constraints. [ABSTRACT FROM AUTHOR]

The pointing consensus problem asks each agent in a multiagent system to agree on their headings toward a common target. This paper proposes a decentralized approach to the pointing consensus problem by simultaneously solving three smaller problems: bearing-only measurement based network localization, target decision, and heading coordination. The proposed solution guarantees that all agents’ headings almost globally asymptotically target any weighted centroid of the agents’ positions. Furthermore, based on this approach, two decentralized solutions for the Fermat–Weber location problem are proposed and analyzed. Simulation results are also provided to support the analysis. [ABSTRACT FROM AUTHOR]

This paper addresses the robust optimal filtering design over unreliable networks, where the data packet dropouts occur during the signal transmission from the sensor side to the filter. The designed filter is expected, under communication data loss, to provide a guaranteed robustness against disturbance/model uncertainty while achieving the minimized variance of the estimation error under Gaussian white noises and the worst case of the disturbance. The Nash game approach is adopted to deal with such a multiobjective filtering problem. Based on the concept of the mean-square stability, Nash equilibrium strategies are analytically applied in terms of two cross-coupled modified algebraic Riccati equations. The presented design method provides a systematic way to achieve a tradeoff of the estimation performance in the $\mathcal {H}_2$ and $\mathcal {H}_\infty$ senses in the presence of data loss. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed set-membership filtering problem for a class of general discrete-time nonlinear systems under event-triggered communication protocols over sensor networks. To mitigate the communication burden, each intelligent sensing node broadcasts its measurement to the neighboring nodes only when a predetermined event-based media-access condition is satisfied. According to the interval mathematics theory, a recursive distributed set-membership scheme is designed to obtain an ellipsoid set containing the target states of interest via adequately fusing the measurements from neighboring nodes, where both the accurate estimate on Lagrange remainder and the event-based media-access condition are skillfully utilized to improve the filter performance. Furthermore, such a scheme is only dependent on neighbor information and local adjacency weights, thereby fulfilling the scalability requirement of sensor networks. In addition, an optimization algorithm is developed to minimize the trace of the estimated ellipsoid set, and the effect from the adopted event-triggered threshold is thoroughly discussed as well. Finally, a simulation example is utilized to illustrate the usefulness of the proposed distributed set-membership filtering scheme. [ABSTRACT FROM AUTHOR]

In recent years, data have played an increasingly important role in the economy as a good in its own right. In many settings, data aggregators cannot directly verify the quality of the data they purchase, nor the effort exerted by data sources when creating the data. Recent work has explored mechanisms to ensure that the data sources share high-quality data with a single data aggregator, addressing the issue of moral hazard. Oftentimes, there is a unique, socially efficient solution. In this paper, we consider data markets where there is more than one data aggregator. Since data can be cheaply reproduced and transmitted once created, data sources may share the same data with more than one aggregator, leading to free-riding between data aggregators. This coupling can lead to nonuniqueness of equilibria and social inefficiency. We examine a particular class of mechanisms that have received study recently in the literature, and we characterize all the generalized Nash (GN) equilibria of the resulting data market. We show that, in contrast to the single-aggregator case, there is either infinitely many GN equilibria or none. We also provide necessary and sufficient conditions for all equilibria to be socially inefficient. In our analysis, we identify the components of these mechanisms that give rise to these undesirable outcomes, showing the need for research into mechanisms for competitive settings with multiple data purchasers and sellers. [ABSTRACT FROM AUTHOR]

This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a solution can be based on prior functions. We show that the problem is well-posed when formulated in a parametric fashion, and that the solution parameter depends continuously on the prior function. In this way, we are able to obtain a smooth parametrization of admissible spectral densities. Based on this result, the problem is reparametrized via a bijective change of variables out of a numerical consideration, and then a continuation method is used to compute the unique solution parameter. Numerical aspects, such as convergence of the proposed algorithm and certain computational procedures are addressed. A simple example is provided to show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the identification of infinite impulse response (IIR) systems with binary-valued measurements. The key to our approach is to recast the initial identification problem into an identification problem in the set-membership framework. This enables us to identify the system using an identification algorithm devoted to IIR systems in such a framework. Although the proposed algorithm is designed for noise free data, an analysis is provided in the presence of noise, and illustrative examples are provided to demonstrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient marking estimation method for a subclass of time labeled Petri nets (TLPNs), in which each transition is associated with an infinite upper bound delay. The unobservable subnet of the considered subclass of TLPNs is backward-conflict-free, and all the output transitions of each conflict place are observable. The highlight of this method is that the markings set consistent with a given observation can be determined by a linear algebraic system based on the so-called slow-bound marking and fast-bound marking pairs. An algorithm to compute an online estimator is provided, and an example is given. By this method, the exhaustive construction of the full state space including the state class graph is avoided. This approach provides guidelines of sensor deployment in the design stage so that the online marking estimation problem can be efficiently solved. [ABSTRACT FROM AUTHOR]

This paper proposes a novel diagnosis technique for discrete event systems (DESs) plant models. The developed diagnosis tool, so called diagnoser, is able to detect and isolate the occurrence of system's faults without the knowledge of the system's past behavior. This allows the diagnoser to asynchronously begin its diagnosis of a system's behavior at any time instance of system operation (including postfault occurrences); consequently removing the generally required synchronous initialization between a diagnoser and the system under diagnosis. The necessary and sufficient conditions are derived for the diagnosability of a given DES plant under this asynchronous situation. Several examples are provided to illustrate the details of the proposed diagnosis framework. [ABSTRACT FROM AUTHOR]

This paper considers the set membership fusion estimation problem for the general multisensor dynamic systems with unknown but bounded noises. In order to achieve the ellipsoidal fusion formulae, we divide the set membership filter problem into two steps: the prediction step and the fusion update step. The proposed method has the following nice properties. First, each step can be converted into a semidefinite programming problem, which can be efficiently computed. Second, part-analytical formulae of the shape matrix and the center of the bounding ellipsoid can be derived by using a decoupled technique, which can significantly reduce the computational complexity. Moreover, the relationship between the fusion center and local sensors can be clearly revealed based on the ellipsoidal fusion formula. Finally, it is interesting that the ellipsoidal fusion formula is similar in form to the classic mean-squared error filter fusion, although they are of the different optimization frameworks. However, the fusion weights of the information matrix provided by the different sensors are different and the optimal fusion weights can be calculated by solving a convex optimization problem. A typical numerical example in target tracking demonstrates the effectiveness of the proposed centralized and distributed fusion formula. [ABSTRACT FROM AUTHOR]

This paper studies multiagent distributed estimation under sensor attacks. Individual agents make sensor measurements of an unknown parameter belonging to a compact set, and, at every time step, a fraction of the agents’ sensor measurements may fall under attack and take arbitrary values. We present the saturated innovation update ($\mathcal{SIU}$) algorithm for distributed estimation resilient to sensor attacks. Under the iterative $\mathcal{SIU}$ algorithm, if less than one half of the agent sensors fall under attack, then, all of the agents’ estimates converge at a polynomial rate (with respect to the number of iterations) to the true parameter. The resilience of $\mathcal{SIU}$ to sensor attacks does not depend on the topology of the interagent communication network, as long as it remains connected. We demonstrate the performance of $\mathcal{SIU}$ with numerical examples. [ABSTRACT FROM AUTHOR]

This paper introduces a general framework for prediction based on nonparametric local estimation and bounding techniques. A set of historic input-output measurements of the system is stored in a database. When a prediction for a given point is required, data from the neighborhood of this point is retrieved and a prediction is formed. These prediction methods return an interval that bounds the considered system output. The width of the obtained interval prediction reflects the amount of information about the system available at the point to be predicted. In addiction, the midpoint of the interval prediction can be used as central estimate. The contribution of the paper is threefold. First, a general framework that covers previous methods proposed in the literature is presented. Second, the general properties of the framework are analyzed. Third, new predictors based on this framework are proposed. Finally, a benchmark example and a comparative study are provided for illustration purposes. [ABSTRACT FROM PUBLISHER]

A parsimonious model is always preferred in engineering applications not only because it has a better prediction ability but also because it suffers less from the curse of dimensionality in data-based modeling. One way to achieve a parsimonious model is to identify contributing variables from the candidate variables and then to eliminate noncontributing or redundant variables. However, identifying which variables contribute and which variables do not contribute is not an easy task for a nonparametric nonlinear system. This paper considers variable-selection problems for a nonlinear nonparametric system. Two approaches, inverse and contour variable-selection algorithms, are proposed along with their theoretical analysis and numerical algorithms. Neither approach suffers from the curse of dimensionality, which is usually a problem for traditional variable-selection methods for a nonparametric nonlinear system. Furthermore, no elliptic symmetry nor independent input variables are assumed, so both algorithms enjoy wide applications. Numerical algorithms for both approaches are fairly straightforward and simple. [ABSTRACT FROM AUTHOR]

We consider the problem of resilient state estimation in the presence of integrity attacks. There are $m$ sensors monitoring the state and $p$ of them are under attack. The sensory data collected by the compromised sensors can be manipulated arbitrarily by the attacker. The classical estimators, such as the least squares estimator, may not provide a reliable estimate under the so-called $(p,m)$ -sparse attack. In this paper, we are not restricting our efforts to studying whether any specific estimator is resilient to the attack or not, but instead we aim to present some generic sufficient and necessary conditions for resilience by considering a general class of convex optimization based estimators. The sufficient and necessary conditions are shown to be tight, with a trivial gap. We further specialize our result to the scalar sensor measurements case and extend our framework to incorporate estimators with correlated cost function optimization. Experimental results tested on the IEEE 14-bus test system validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Distributed estimation has proven to be suitable for many multiagent system (MAS) applications, yet it relies heavily on information exchange via a costly and vulnerable communication network. This paper proposes a sensing-based distributed estimation algorithm that enables a local monitoring agent to expand its estimation capabilities beyond its sensing range without needing communication overhead. The key to expanding the limited sensing range is to incorporate the MAS's cooperative control protocol, allowing the monitoring agent to infer the state of out-of-range agents from the behavior of in-range agents that may interact with them. Then, the state estimation for out-of-range agents is performed through a Bayesian approach that considers the correlation of state estimates between in-range and out-of-range agents. This approach of only taking sensor measurements of local monitoring agents without interagent communications can successfully compensate for the existing communication-based distributed estimation methods. The performance of the proposed sensing-based distributed estimation algorithm is theoretically verified and demonstrated with numerical simulations of a multivehicle formation flight example. [ABSTRACT FROM AUTHOR]

This paper considers the input-to-state stability (ISS) of time-varying switched systems with time delays, where the upper bound estimation for the operator of Lyapunov function (UBEOL) is assumed to be time varying and mode dependent. The ISS and integral ISS are investigated for time-varying switched systems with time delays by using the Lyapunov–Razumikhin and comparison theorem methods. Since the coefficient in the UBEOL is time varying and takes a positive/negative value, the subsystems consist of both ISS and non-ISS subsystems, simultaneously. It is shown that our presented results have wider applications than some existing works. Two examples, including one of the consensus for time-varying multiagent systems with cooperative and competitive protocols, are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The time and measurement update for the discrete time Kalman filter can be formulated in terms of conditional means and covariances. The unscented Kalman filter can be interpreted as calculating these conditional means and covariances by using the unscented transform. This approach can also be directly applied to nonlinear models as an alternative to the discrete time extended Kalman filter. In this paper, a novel method for computing the unscented Kalman filter for a nonlinear model with continuous time dynamics and discrete time measurements is presented. Compared to the existing approaches, this method is far simpler and less computationally demanding, and it performs at least as well. [ABSTRACT FROM AUTHOR]

This paper generalizes Thompson and Hilbert metrics to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. The corresponding distances are filtering invariant, can be computed efficiently, and admit geodesic paths that preserve rationality; these are properties of fundamental importance in many engineering applications. [ABSTRACT FROM AUTHOR]

This paper concerns the nonparametric identification problem for a class of nonlinear discrete-time dynamical systems that is characterized by its cascade structure. This is a Hammerstein system being a series connection of a nonlinear memoryless element followed by a linear dynamic system. The input–output training data generated from the system are dependent and they do not reveal the strong mixing property. The nonlinear part of the system is recovered with the weighted $k$ -nearest neighbor regression estimate. The a priori information is nonparametric, both the nonlinear characteristic and the impulse response of the linear part are completely unknown and can be of any form. Local and global properties of the estimate are examined. Whatever the probability density of the input signal, the estimate converges at every continuity point of the characteristic as well as in the global sense. We derive the formulas for asymptotic bias and the variance and evaluate the corresponding rate of convergence. The convergence rate is independent of the shape of the input density and is proved to be optimal. These results allow us to find a set of optimal nonnegative weights that further improve the accuracy of our estimation algorithm. Our findings are supported by simulation experiments. [ABSTRACT FROM AUTHOR]

This paper concerns the nonlinear Korteweg-de Vries equation with boundary time-delay feedback. Under appropriate assumption on the coefficients of the feedbacks (delayed or not), we first prove that this nonlinear infinite dimensional system is well posed for small initial data. The main results of our study are two theorems stating the exponential stability of the nonlinear time-delay system. Two different methods are employed: a Lyapunov function approach (allowing to have an estimation on the decay rate, but with a restrictive assumption on the length of the spatial domain of the KdV equation) and an observability inequality approach, with a contradiction argument (for any noncritical lengths but without estimation on the decay rate). Some numerical simulations are given to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a general class of distributed constrained optimization problems over a multiagent network, where the global objective function is represented by the sum of all local objective functions. Each agent in the network only knows its own local objective function, and is restricted to a global nonempty closed convex set. We discuss the scenario where the communication of the whole multiagent network is expressed as a sequence of time-varying general unbalanced directed graphs. The directed graphs are required to be uniformly jointly strongly connected and the weight matrices are only row-stochastic. To collaboratively deal with the optimization problems, existing distributed methods mostly require the communication graph to be fixed or balanced, which is impractical and hardly inevitable. In contrast, we propose a new distributed projection subgradient algorithm which is applicable to the time-varying general unbalanced directed graphs and does not need each agent to know its in-neighbors’ out-degree. When the objective functions are convex and Lipschitz continuous, it is proved that the proposed algorithm exactly converges to the optimal solution. Simulation results on a numerical experiment are shown to substantiate feasibility of the proposed algorithm and correctness of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the interacting multiple model (IMM) estimator for networked control systems with packet loss but without packet acknowledgment (ACK). The ACK is a signal sent by the actuator to inform the estimator of whether control packets are lost or not. A system with ACK is usually called a transmission control protocol (TCP) like system; otherwise, it is called a user datagram protocol (UDP) like system. We show that the stability of the IMM estimator for UDP-like systems is determined by the observation packet arrival rate (p.a.r.) and is independent of the control p.a.r. and control inputs. The IMM estimator is stable if the observation p.a.r. is greater than a critical value. We show that this critical value is the same as the critical value for the stability of the optimal estimator for its corresponding TCP-like system. If control inputs eventually tend to zero, the error covariance of the IMM estimator converges to that of the optimal estimator for TCP-like systems. We characterize the impact of the control/observation p.a.r. and the control input on estimation performance. Finally, we prove that the average estimation performance of the IMM estimator approximates that of the optimal estimator within a finite bound, and is superior to that of the linear minimum mean square error estimator. [ABSTRACT FROM AUTHOR]

In this paper, we address the identification of two-dimensional (2-D) spatial-temporal dynamical systems described by the Vector-AutoRegressive (VAR) form. The coefficient-matrices of the VAR model are parametrized as sums of Kronecker products. When the number of terms in the sum is small compared to the size of the matrices, such a Kronecker representation efficiently models large-scale VAR models. Estimating the coefficient matrices in least-squares sense gives rise to a bilinear estimation problem that is tackled using an Alternating Least Squares (ALS) algorithm. Regularization or parameter constraints on the coefficient-matrices allows to induce temporal network properties, such as stability, as well as spatial properties, such as sparsity or Toeplitz structure. Convergence of the regularized ALS is proved using fixed-point theory. A numerical example demonstrates the advantages of the new modeling paradigm. It leads to comparable variance of the prediction error with the unstructured least-squares estimation of VAR models. However, the number of parameters grows only linearly with respect to the number of nodes in the 2-D sensor network instead of quadratically in the case of fully unstructured coefficient-matrices. [ABSTRACT FROM AUTHOR]

This paper studies the consensus of multiagent systems with binary-valued communication. We consider a group of agents on an undirected graph with a fixed topology, differing from most existing work, the information each agent gets from its neighbors are binary-valued measurements with stochastic noises. A two-time-scale protocol that alternates estimation and control is constructed: Each agent in the system estimates the states of its neighbors’ based on the binary-valued measurements for a dwelt time, during which every agent's state will keep constant; Based on the estimations of its neighbors’ states and its own state, each agent designs its own control, by which the state will be updated and then repeats the process of estimation alternating with control. For the state estimation, we propose an identification algorithm without truncation, which is analyzed to be convergent and the convergence rate is given. By the two-time-scale protocol, the system is shown to achieve weak consensus and mean square consensus by using a stochastic Lyapunov analysis and the consensus speed is given. Simulations are given with different holding time, which are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of providing a complete parametrization of the minimal spectral factors of a discrete-time rational spectral density is considered. The desired parametrization, given in terms of the all-pass divisors of a certain all-pass function, is established in the most general setting: after several partial results, mostly in the continuous-time case, this is indeed the first complete parametrization obtained without resorting to any facilitating assumption. This result provides a positive answer to a conjecture raised in 2016. [ABSTRACT FROM AUTHOR]

Given a set of target detections over several time periods, this paper addresses the multitarget tracking (MTT) problem of optimally assigning detections to targets and estimating the trajectory of the targets over time. MTT has been studied in the literature via predominantly probabilistic methods. In contrast, we propose the use of mixed integer optimization (MIO) along with relaxations and local-search-based heuristic algorithms that are: scalable, as they provide near optimal solutions for six targets and ten time periods in milliseconds to seconds; general, as they make no probabilistic assumptions on the detection process; robust, as they can accommodate missed and false detections of the targets; and easily implementable, as they use at most two tuning parameters. We evaluate the performance of the new methods using a novel metric for the complexity of an instance, and find that they provide high quality solutions both reliably and quickly for a large range of scenarios, resulting in a promising approach to the area of MTT. [ABSTRACT FROM AUTHOR]

This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature. [ABSTRACT FROM AUTHOR]

This paper focuses on a stochastic formulation of Bayesian attitude estimation on the special orthogonal group. In particular, an exponential probability density model for random matrices, referred to as the matrix Fisher distribution, is utilized to represent the uncertainties of attitude estimates and measurements in a global fashion. Various stochastic properties of the matrix Fisher distribution are derived on the special orthogonal group, and based on these, two types of intrinsic frameworks for Bayesian attitude estimation are constructed. These avoid complexities or singularities of the attitude estimators developed in terms of quaternions. The proposed approaches are particularly useful to deal with large estimation errors or large uncertainties for complex attitude maneuvers. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of modes detection for switching discrete-time linear and affine systems. A unified presentation of the model-based methods with the corresponding modes detectors is carried out and a comparative study is conducted. Next, the different notions of discernibility proposed in the literature are presented. Such notions are central since they guarantee the uniqueness of the solution delivered by the modes detectors. A complete step-by-step procedure of modes detection is proposed. The paper includes, whenever necessary, some extensions of the existing results. [ABSTRACT FROM AUTHOR]

In this paper, we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting, where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function, and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of deterministic error bounds, and establishes guaranteed estimates, thus being in principle better suited for the use in control design. However, a main limitation of such deterministic bounds lies in their potential conservatism, thus leading to estimates of restricted use. In this paper, we propose a rapprochement between the stochastic and worst-case system identification viewpoints, which is based on the probabilistic setting of information-based complexity. The main idea in this line of research is to “discard” sets of measure at most $\epsilon$, where $\epsilon$ is a probabilistic accuracy, from the set of deterministic estimates. Therefore, we are decreasing the so-called worst-case radius of information at the expense of a given probabilistic “risk.” In the case of uniformly distributed noise, we derive new computational results, and in particular we compute a trade-off curve, called violation function, which shows how the radius of information decreases as a function of the accuracy. To this end, we construct randomized and deterministic algorithms which provide approximations of this function. We report extensive simulations showing numerical comparisons between the stochastic, worst-case and probabilistic approaches, thus demonstrating the efficacy of the methods proposed in this paper. [ABSTRACT FROM AUTHOR]

In this  paper, we study the prediction performance of the Kalman filter (KF) in a worst case minimax setting as studied in online machine learning, information, and game theory. The aim is to predict the sequence of observations almost as well as the best reference predictor (comparator) sequence in a comparison class. We prove worst-case bounds on the cumulative squared prediction errors using a priori knowledge about the complexity of reference predictor sequence. In fact, the performance of the KF is derived as a function of the performance of the best reference predictor and the total amount of drift that occurs in the schedule of the best comparator. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of Kalman filtering over Gilbert–Elliott channels where random packet drops follow a time-homogeneous two-state Markov chain whose state transition is determined by a pair of failure and recovery rates. First of all, we establish a relaxed condition guaranteeing peak-covariance stability described by an inequality in terms of the spectral radius of the system matrix and transition probabilities of the Markov chain. We further show that the condition can be interpreted using a linear matrix inequality feasibility problem. Next, we prove that the peak-covariance stability implies mean-square stability, if the system matrix has no defective eigenvalues on the unit circle. This connection between the two stability notions holds for any random packet drop process. We prove that there exists a critical curve in the failure-recovery rate plane, below which the Kalman filter is mean-square stable and no longer mean-square stable above. Finally, a lower bound for this critical failure rate is obtained making use of the relationship we establish between the two stability criteria, based on an approximate relaxation of the system matrix. [ABSTRACT FROM PUBLISHER]

This paper generalizes the well-known covariance intersection algorithm for distributed estimation and information fusion of random vectors. Our focus will be on partially correlated random vectors. This is motivated by the restriction of the standard covariance intersection algorithm, which treats all random vectors with arbitrary cross correlations and the restriction of the classical Kalman filter, which requires complete knowledge of the cross correlations. We first give a result to characterize the conservatism of the standard covariance intersection algorithm. We then generalize the covariance intersection algorithm to two random vectors with a given correlation coefficient bound and show in what sense the resulting covariance bound is tight. Finally, we generalize the notion of correlation coefficient bound to multiple random vectors and provide a covariance intersection algorithm for this general case. Our results will make the already popular covariance intersection more applicable and more accurate for distributed estimation and information fusion problems. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of fault classification when different fault classifiers are performed simultaneously. Based on spectral meta-learner (SML) proposed by Parisi et al., its recursive version, i.e., recursive SML (RSML) is developed for online combining the potentially conflicting classification information. Considering different statistical properties of faults occurring at different time intervals, the binary classification information is recursively utilized. By introducing a forgetting factor, the leading eigenvector of the estimate of the time-varying covariance matrix is used as the weight vector for each classifier. Rank-one modification is then used for calculating the eigenvector in order to reduce the online computational complexity. The performance of RSML is strictly analyzed in a statistical sense, including the effect of recursive calculation and conditional dependence of different classifiers on the weight vector. Compared with majority voting and SML, a higher balanced accuracy of RSML can be verified by the benchmark Tennessee Eastman process. [ABSTRACT FROM PUBLISHER]

In this paper, we address the problem of controlling a network of mobile sensors so that a set of hidden states are estimated up to a user-specified accuracy. The sensors take measurements and fuse them online using an information consensus filter (ICF). At the same time, the local estimates guide the sensors to their next best configuration. This leads to an LMI-constrained optimization problem that we solve by means of a new distributed random approximate projections method. The new method is robust to the state disagreement errors that exist among the robots as the ICF fuses the collected measurements. Assuming that the noise corrupting the measurements is zero-mean and Gaussian and that the robots are self-localized in the environment, the integrated system converges to the next best positions from where new observations will be taken. This process is repeated with the robots taking a sequence of observations until the hidden states are estimated up to the desired user-specified accuracy. We present simulations of sparse landmark localization, where the robotic team achieves the desired estimation tolerances while exhibiting interesting emergent behavior. [ABSTRACT FROM PUBLISHER]

In this paper, source localization by a network of primitive binary sensors under various imperfections are studied. Detailed analysis and mathematical modeling of imperfect binary sensors are presented. Imperfections include sensor failures of two types, drifting, uncertainty, and heterogeneity in binary sensor trigger thresholds, presence of noise, and nonradial symmetry of sensing ranges. Theoretical results, including asymptotical convergence, are established, in particular in the presence of substantial outliers due to sensor failure and large noise. Efficient numerical algorithms are proposed and simulated supporting the theoretical analysis. [ABSTRACT FROM PUBLISHER]

This paper presents a noise adaptive variational Bayesian cubature information filter based on Wishart distribution. In the frame of recursive Bayesian estimation, the noise adaptive information filter propagating the information matrix and information state is derived. And the integration of recursive Bayesian estimation is approximated by cubature integration rule. Then, the inverse of measurement noise matrix is modeled as a Wishart distribution, so the joint distribution of posterior state and measurement noise can be approximated by the product of independent Gaussian and Wishart. Furthermore, the corresponding square root version is also derived to improve numerical characteristics. Simulation results with unknown and correlated measurement noise demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Most of time-varying systems in fusion estimation are generally modeled without bounded noises. In this paper, we study the distributed fusion estimation problem for networked time-varying systems with bounded noises, where the resource constraints (i.e., bandwidth or energy) and quantization effect are described by a unified model. A new local estimator with time-varying gain is designed by solving a class of convex optimization problems such that the square error of the estimator is bounded. When each local estimate is transmitted to the fusion center over communication networks, the selection probability criterion is derived such that the mean square error of the each compensating state estimate is bounded. Then, a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Target tracking system with time-varying sampling period is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an iterative residual generator (IRG) is proposed for discrete time-invariant state–space model with the aim of detecting faulty signals. By minimizing the mean square errors subject to unbiasedness constraint, a new filter with finite impulse response structure is derived. The resulting IRG is then obtained by extracting residual signal from the batch filter through several predictor/corrector iterations. It shows that IRG can provide a zero-mean Gaussian process regardless of previous estimation errors. More importantly, it includes the residual generation process in the Kalman filter as its special case. With the chi-square test, a numerical example is simulated to demonstrate that IRG can reduce the false alarm significantly compared with the traditional recursive strategy in the presence of actuator or sensor faults, and the estimation horizon length in IRG serves as a tuning parameter providing a tradeoff between the missed alarm and false alarm. [ABSTRACT FROM AUTHOR]