Set-membership Theory Research Articles

Attack Detection of Complex Cyber-Physical Networks via Set-Membership Theory

This paper investigates the attack detection of complex cyber-physical networks (CCPNs) based on the set-membership theory and moving-target defense strategy. Firstly, a moving-target defense (MTD) strategy is proposed to prevent attackers from stealing the system model, which can improve the security of systems. Secondly, a robust observer based on the MTD strategy is designed to estimate the system states without attacks. Meanwhile, we combine the set-membership and interval hull theorem to calculate the reachable set of the states and dynamic thresholds of the residual system in the absence of attacks. Then, an attack detector is established to give an alarm of false data injection (FDI) attacks by comparing the actual residual signal under attacks and the dynamic thresholds. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Distributed Fusion Estimation for the Measurements with Bounded Disturbances

Abstract The information fusion problem is studied for multi-sensor systems in the presence of bounded disturbances. In this paper, a distributed fusion estimation algorithm is proposed based on the set-membership theory, which obtains the overall estimates based on multi-ellipsoids intersection. A parameter adaptive adjustment scheme is derived to guarantee the performance of the algorithm. The feedback mechanism is also introduced to enhance the estimation procedure. Through theoretical analysis and simulation, the performance of the proposed algorithm is analyzed, and some interesting properties of the proposed algorithm are proved. Results show that the proposed algorithm improves the point estimation accuracy. Compared with the algorithm without feedback, the one with feedback has better local estimation. Meanwhile, the effectiveness of the proposed algorithm in improving state estimation accuracy has been proved by the simulation results.

A set membership theory based parameter and state of charge co-estimation method for all-climate batteries

State of charge estimation of the battery is one of the core functions in the battery management system. Accurate and reliable state of charge estimation under wide temperature range is critical for the application of all-climate electric vehicles. The main work of this paper is as follows: (1) To achieve accurate closed-loop state estimation, a temperature dependent battery model is proposed; (2) The common model-based state of charge estimation methods using filters like Kalman filter assume that the state perturbations and measurement noise are white and Gaussian noises, which is not realistic in practical application. To solve this problem, set membership method which holds that the noises are unknown but bounded is used for state of charge estimation. Based on the established temperature dependent battery model and the set membership method, battery parameter and state of charge co-estimation algorithm is proposed for all-climate battery state estimation; (3) The proposed method is fully verified at −10 °C–40 °C and the comparison between the proposed method and extended Kalman filter is conducted to illustrate its superiorities. Furthermore, the validity and real time performance of the co-estimation method are verified in a hardware-in-loop test bench. Results show that the proposed co-estimation method has excellent robustness and the state of charge estimation error is bounded to 5% under wide temperature range.

Centralized Fusion Methods for Multi-Sensor System With Bounded Disturbances

The set-membership information fusion problem is studied for general multi-sensor dynamic systems. Based on set-membership theory, three centralized state fusion estimation algorithms in the presence of bounded disturbances are proposed, namely augmented algorithm, combined measurement filtering algorithm and pseudo-sequential filtering algorithm. Theoretical discussions on the convergence and boundedness of the proposed fusion algorithms are provided and their stability is proved. The estimate accuracy, computational complexity and flexibility of these three fusion algorithms are compared through theoretical analysis and simulation. And their exchanging property of measurement update order is discussed. Results show that these algorithms are functionally equivalent in terms of the estimation accuracy and the exchangeability of the measurement update order can be guaranteed as long as the parameters satisfy certain conditions. Meanwhile the simulation results prove the role of the proposed algorithms in improving state estimation accuracy. In addition, the combined measurement filtering algorithm has the highest calculation speed due to lower dimension. But it is less flexible because the sensor measurement matrices need to satisfy some additional conditions. These conclusions are valuable in applications.

Set-Membership-Based Fault Detection and Isolation for Robotic Assembly of Electrical Connectors

This paper addresses the fault detection and isolation (FDI) problem for robotic assembly of electrical connectors in the framework of set-membership. Both the fault-free and faulty cases of assembly are modeled by different switched linear models with known switching sequences, bounded parameters, and external disturbances. The locations of switching points of each model are assumed to be inside some areas but the accurate positions are not clear. Given current input/output data, the feasible parameter set of fault-free switched linear model is obtained by sequentially calculating an optimal ellipsoid. If the pair of data is not consistent with any possible submodel, a fault is then detected. The isolation of fault is realized by checking the consistency between the data sequence and each possible fault model one by one. The robustness of the proposed FDI algorithms is proved. The effectiveness of these algorithms is verified by the robotic assembly experiments of mating electrical connectors. Note to Practitioners —In modern robotic assembly tasks, the industrial robots often need to manipulate tiny objects with complex structure. Electrical connectors are a typical kind of these objects and widely used in many industrial fields. To avoid damaging the fragile connectors and accelerate the assembly process, it is required to promptly detect and isolate the certain assembly fault in real time so that the robot can immediately implement an error recovery procedure according to the identified fault. The proposed set-membership-based fault detection and isolation (FDI) methodology satisfies both the timing and fault-isolation requirements for this kind of robotic assembly task. In terms of the set-membership theory, no false alarm will occur if there are sufficient training data for the proposed method. In addition, it turns out that the proposed method can signal an alarm faster than conventional residual-based FDI method from plentiful experiments. Although only the robotic assembly of electrical connectors is investigated, our FDI method can also be applied in the assembly task of other small and complex parts. This is especially useful for increasing the productivity and promoting the automation level of electronic industries.

Unified Set Membership theory for identification, prediction and filtering of nonlinear systems

The problem of making inferences from data measured on nonlinear systems is investigated within a Set Membership (SM) framework and it is shown that identification, prediction and filtering can be treated as specific instances of the general presented theory. The SM framework presents an alternative view to the Parametric Statistical (PS) framework, more widely used for studying the above specific problems. In particular, in the SM framework, a bound only on the gradient of the model regression function is assumed, at difference from PS methods which assume the choice of a parametric functional form of the regression function. Moreover, the SM theory assumes only that the noise is bounded, in contrast with PS approaches, which rely on noise assumptions such as stationarity, uncorrelation, type of distribution, etc. The basic notions and results of the general inference making theory are presented. Moreover, some of the main results that can be obtained for the specific inferences of identification, prediction and filtering are reviewed. Concluding comments on the presented results are also reported, focused on the discussion of two basic questions: what may be gained in identification, prediction and filtering of nonlinear systems by using the presented SM framework instead of the widely diffused PS framework? why SM methods could provide stronger results than the PS methods, requiring weaker assumptions on system and on noise?

A new NLMS algorithm for slow noise magnitude variation

A set-membership (SM) normalized least-mean-square (NLMS) (SMNLMS) algorithm is developed using SM theory in the class of optimal bounding ellipsoid (OBE) algorithms. This signed version of NLMS algorithm requires a priori knowledge of a bound for the error magnitude, which is unknown in most applications. A very simple algorithm is proposed for the case in which the unknown magnitude of the measurement noise is slowly time-varying. The proposed algorithm is able to extract the noise magnitude information and exploit this magnitude to enhance or accelerate the learning process without risk of overbounding or performance loss due to underbounding. The performance of the proposed algorithm is compared with that of SMNLMS using some simulation examples.

Linear prediction analysis of speech based on set-membership theory

When computing linear prediction (LP) parameters of speech, large numbers of data are uninformative in a certain set-theoretic sense, and the expense of updating the estimates at these times can be avoided. “Set-membership” (SM) identification is formulated as a weighted recursive covariance LP problem with a special criterion for dynamic weight determination. An algorithm is developed which can be implemented on a systolic processor if desired, but which retains a simple interpretation as a specially weighted convariance LP method. The algorithm is applied to identification of the LP parameters of real speech data, and a number of practical issues are discussed. The potential for an adaptive strategy and other open research questions generated by the experimental work are discussed in the conclusions.