Set-membership State Estimation Research Articles

Set-membership state estimation for time-varying complex networks: two zonotopic design methods

This article studies the zonotopic set-membership state estimation problem for linear time-varying complex networks with unknown-but-bounded (UBB) noises, where the UBB noises are contained by a set of zonotopes. The objective of the addressed problem is to give two design methods, namely the correction matrix method and the state observer method, where a time-varying zonotopic sequence containing all possible states of the system is obtained. The expressions of the correction matrix and the observer gain are given under the F-radius criterion, and the desired minimum zonotopes are obtained. In addition, a state observer based on the measured output at the current moment is designed to analyze the equivalence between the above two methods. Finally, in order to demonstrate the effectiveness of the proposed state estimation algorithms, two simulation examples are presented.

Event-Based Distributed Set-Membership Estimation for Complex Networks Under Deception Attacks

This paper addresses the problem of event-based distributed set-membership estimation for complex networks with unknown but bounded (UBB) disturbances. To reflect the compromised data transmissions in cyber security, deception attacks are taken into consideration. Meanwhile, a novel estimation model is proposed against UBB disturbances. In order to schedule the signal transmissions between nodes and remote estimators, a novel decentralized dynamic periodic event-triggered mechanism (DPETM) with a time-varying threshold is developed for each node of the complex networks, which reduces the waste of communication resources and the complexity of computation. Thereafter, a series of distributed set-membership estimators are designed, whose parameters are explicitly determined in terms of the resolution of a particular linear matrix inequality (LMI) related to the information of the communication topology. An optimized ellipsoid estimation set is obtained by applying a recursive optimization algorithm. Finally, the simulation results are shown to demonstrate the viability of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by set-membership state estimation problem of complex networks in practical missions, such as military, environment, industry, etc. The set-membership estimation of complex networks provides a reliable confidence region for each system node. Event-triggered control is an effective method for the design of set-membership estimator. But the common results require the systems to monitor the measurements point-to-point, which leads to the huge consumption of calculation and communication resources. For this reason, this paper originally extends the DPETM to the discrete-time version from the field of continuous-time systems. Meanwhile, this paper considers the deception attacks in communication channels, and the generic framework established earlier can tackle simultaneously sector-bounded nonlinearity, UBB disturbances, and deception attacks. The main difficulty of this paper lies in the analysis for the sawtooth constraint of periodic samplings. For this difficulty, we introduce a piecewise auxiliary function, which is similar with the loop-function in the field of continuous-time systems. Together with recursive optimization algorithm, the detailed analysis method is proposed for the reliable confidence regions of each set-membership estimator.

Set-valued state estimators for a class of uncertain discrete-time nonlinear systems

Set-membership state estimation problem for a certain class of discrete-time nonlinear systems is tackled in this work. First, this problem is formulated as a reachability analysis problem. Then, to avoid the wrapping effect, explicit expression of the general solution of this class of systems is used to design new set-valued state estimation schemes. Moreover, for practical considerations, two periodically re-initialized algorithms based on both interval analysis and zonotope computation are introduced. The merit of the proposed approach is illustrated on a numerical example and its performance is compared to that of other methods borrowed from the literature.

Event-Triggered Set-Membership State Estimation for Discrete Delayed Linear Systems over Sensor Networks

Event-Triggered Set-Membership State Estimation for Discrete Delayed Linear Systems over Sensor Networks

Set Membership State Estimation with Quantized Measurements and Optimal Threshold Selection

The problem of state estimation with quantized measurements is addressed in the set membership estimation setting. The main contribution concerns the optimal selection of the quantizer thresholds in order to minimize the worst-case radius of the feasible state set. This allows one to design adaptive quantizers reducing the uncertainty associated to the state estimates. The proposed solution is applied to several outer approximations of the feasible sets, based on parallelotopes, zonotopes and constrained zonotopes. The benefits of the threshold selection mechanism are assessed on a numerical example, highlighting the trade off between computational burden and uncertainty reduction.

Set-Membership State Estimation for Multirate Nonlinear Complex Networks Under FlexRay Protocols: A Neural-Network-Based Approach.

In this article, the set-membership state estimation problem is investigated for a class of nonlinear complex networks under the FlexRay protocols (FRPs). In order to address practical engineering requirements, the multirate sampling is taken into account which allows for different sampling periods of the system state and the measurement. On the other hand, the FRP is deployed in the communication network from sensors to estimators in order to alleviate the communication burden. The underlying nonlinearity studied in this article is of a general nature, and an approach based on neural networks is employed to handle the nonlinearity. By utilizing the convex optimization technique, sufficient conditions are established in order to restrain the estimation errors within certain ellipsoidal constraints. Then, the estimator gains and the tuning scalars of the neural network are derived by solving several optimization problems. Finally, a practical simulation is conducted to verify the validity of the developed set-membership estimation scheme.

Secure State Estimation for Artificial Neural Networks With Unknown-But-Bounded Noises: A Homomorphic Encryption Scheme.

This article is concerned with the secure state estimation problem for artificial neural networks (ANNs) subject to unknown-but-bounded noises, where sensors and the remote estimator are connected via open and bandwidth-limited communication networks. Using the encoding-decoding mechanism (EDM) and the Paillier encryption technique, a novel homomorphic encryption scheme (HES) is introduced, which aims to ensure the secure transmission of measurement information within communication networks that are constrained by bandwidth. Under this encoding-decoding-based HES, the data being transmitted can be encrypted into ciphertexts comprising finite bits. The emphasis of this research is placed on the development of a secure set-membership state estimation algorithm, which allows for the computation of estimates using encrypted data without the need for decryption, thereby ensuring data security throughout the entire estimation process. Taking into account the unknown-but-bounded noises, the underlying ANN, and the adopted HES, sufficient conditions are determined for the existence of the desired ellipsoidal set. The related secure state estimator gains are then derived by addressing optimization problems using the Lagrange multiplier method. Lastly, an example is presented to verify the effectiveness of the proposed secure state estimation approach.

Distributed set-membership state estimation based on a zonotope method for linear parameter-varying systems

Distributed set-membership state estimation based on a zonotope method for linear parameter-varying systems

Set-Membership State Estimation for 2-D Roesser Systems Based on Zonotope Radius and Its Application

Set-Membership State Estimation for 2-D Roesser Systems Based on Zonotope Radius and Its Application

Set membership state estimation for discrete-time linear systems with binary sensor measurements

This paper addresses the problem of state estimation for discrete-time linear systems, based on measurements provided by an output binary sensor. The problem is formulated and solved in a set theoretic framework. Two algorithms are devised for recursively computing outer approximations of the set of state vectors compatible with the information provided by the binary sensor. This allows one to obtain a nominal state estimate and to characterize the associated uncertainty. The procedures can be tuned to suitably trade off the quality of set approximations and the required computational load. An input design technique based on the computed feasible state sets, which is aimed at promoting uncertainty reduction, is provided. The case of time-varying sensor threshold is also considered and a strategy for selecting online the value of the threshold is formulated. All the proposed methods are validated in simulations on two numerical examples.

Adaptive Set-Membership State Estimation for Nonlinear Systems Under Bit Rate Allocation Mechanism: A Neural-Network-Based Approach.

In this article, the adaptive neural-network-based (NN-based) set-membership state estimation problem is studied for a class of nonlinear systems subject to bit rate constraints and unknown-but-bounded noises. The measurement output signals are transmitted from sensors to a remote estimator via a bit rate constrained communication channel. To relieve the communication burden and ameliorate the state estimation accuracy, a bit rate allocation mechanism is put forward for the sensor nodes by solving a constrained optimization problem. Subsequently, through the NN learning method, an NN-based set-membership estimator is designed to determine an ellipsoidal set that contains the system state, where the proposed estimator relies upon a prediction-correction structure. With the help of the mathematical induction technique and the set theory, sufficient conditions are obtained to ensure the existence of both the adaptive tuning parameters and the set-membership estimators, and then, the corresponding parameters and estimator gains are calculated by solving a set of optimization problems. In addition, the monotonicity of the upper bound on the squared estimation error with respect to the bit rate and the convergence of the NN weight are analyzed, respectively. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed state estimation algorithm.

Tight set-valued state estimation by combining reachability analysis and set-filtering approaches

In this work, a new approach to design set-valued state estimator for linear discrete-time systems subject to additive and bounded process and measurement uncertainties is proposed. First, the system state equation is rewritten to obtain a stable numerical scheme on which an explicit reachability method is developed, based on zonotopic set computation and a re-initialization procedure. Then, to enhance the accuracy of the computed reachable set, a set-filtering technique is designed based on the system output equation and its intrinsic invariant relationships. The implementation of this filtering method is based on interval analysis coupled to contractor algorithms. The convergence property of the proposed set-valued state estimator is shown under the classical detectability assumption of linear systems. Some simulation results are presented to show the merit of the proposed new set-membership state estimation approach.

Probability-guaranteed state estimation for nonlinear delayed systems under mixed attacks

In this paper, the problem of the networked set-membership state estimation is discussed for a class of nonlinear discrete time-varying systems subject to cyber attacks and time delays. Two forms of malicious attacks (i.e. Denial-of-Service (DoS) attack and bias injection attack) are taken into account to describe the adversary's attempt to destroy/deteriorate the system performance via communication network. It is the aim of the investigated issue to propose a set-membership state estimator ensuring the required estimation performance despite the existence of both the external mixed attacks and internal time delays. By resorting to the feasibility of a series of matrix inequalities, sufficient conditions are provided for the solvability of the addressed state estimator design problem. Furthermore, an optimisation strategy is developed with the purpose of seeking the local optimal estimator parameters. At last, a numerical simulation example is presented to demonstrate the effectiveness of the proposed theoretical algorithm.

Distributed set-membership state estimation based on a zonotope method for linear parameter-varying systems

Distributed set-membership state estimation based on a zonotope method for linear parameter-varying systems

Zonotopic Set-Membership State Estimation for Switched LPV Systems

This paper addresses the state estimation problem for switched discrete-time Linear Parameter Varying (LPV) systems with mensurable and unmeasurable scheduling parameters. A zonotopic switched polytopic state estimator, considering parameter uncertainty, is proposed based on a Set-Membership Approach (SMA). Taking Average Dwell Time (ADT) into account, a new criterion is proposed to guarantee the convergence of the estimation. An application to vehicle lateral dynamics state estimation is used as case study. Simulation results reveal the effectiveness of the proposed algorithm and demonstrate advantages over the existing methods.

Zonotopic Set-Membership State Estimation for Switched Systems With Restricted Switching

In this article, a novel set-membership state estimation method based on zonotopes is proposed for switched systems subject to unknown-but-bounded disturbance with average dwell time (ADT) switching. By testing the consistency between the system model and measured output, an intersection zonotope is constructed based on mode-dependent and semitime-dependent correction matrix. Then, by constructing semitime-dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> -radius functions, the issue of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{\infty }$</tex-math></inline-formula> disturbance attenuation performance for the intersection zonotope is addressed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.

Set-membership state and parameter estimation for discrete time-varying systems based on the constrained zonotope

In this paper, the set-membership state and parameter estimation problems are considered for linear time-varying systems. The noises in the system are unknown but bounded and the variation of parameters is considered as a bounded expansion. The entire estimator is an interactive estimation of parameters and states. In parameter estimation, the exact set of parameter estimates may be non-convex because of the uncertain states. A polytopic linear parameter varying (LPV) enclosure of the system regression expression is constructed as a convex relaxation. The result of parameter estimation is a set to include the true parameter of the model. Meanwhile, in the state estimation, a similar LPV enclosure of the state-space model is also used to bound the state matrix uncertainties. This LPV enclosure in the state estimation is narrowed by the parameter estimation, and then the set of state estimates is computed to include the true state. The constrained zonotope (CZ) is used to describe sets of interest and the necessary set operations are expanded to LPV mapping. Because of the highly adjustable accuracy of CZ, the proposed algorithm can make a better trade-off between computational accuracy and efficiency. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.

Zonotopic set-membership state estimation for switched systems

This paper proposes a new approach for set-membership state estimation of switched discrete-time linear systems subject to bounded disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed and a new criterion is proposed to reduce the size of the zonotope at each sample time. The zonotopic set-membership estimator design for switched systems is provided within the LMI framework. The extension of the proposed scheme to deal with unknown inputs is also presented. An application to vehicle lateral dynamics state estimation is provided. Simulation results demonstrate the effectiveness of the proposed algorithm and highlight its advantages over the existing methods.

Event-triggered interval-based state estimator for continuous-time linear systems

In this paper we propose an interval-based state estimator for continuous-time linear systems with discrete-time measurements using an event-triggered mechanism and an explicit reachability method. An output injection method combined with a state variables permutation procedure are applied to design the robust estimator. In addition, the convergence of the proposed set-membership state estimator and the existence of a lower bound on the inter-event times are shown. Throughout a numerical example, the performance of this estimator are illustrated and compared to related works.

Zonotopic set-membership state estimation for multirate systems with dynamic event-triggered mechanisms

This paper is concerned with the dynamic event-triggered set-membership state estimation issue for a class of multirate networked systems subject to unknown but bounded disturbance and noise. To economize the limited communication resource when performing the desired networked estimation task, a dynamic event-triggered transmission mechanism is proposed to significantly reduce the frequency of sensor data transmissions. A key issue of the addressed problem is to construct a zonotopic outer approximation set to bound the set of states that are consistent with the disturbed system model and the noisy measured outputs. With the help of a prediction-update-correction method, we design a zonotope that is guaranteed to enclose all possible system states due to the unknown disturbance and noise. Then, the size of such a zonotope is minimized by properly designing an introduced correlation matrix at each iteration. Subsequently, the estimation performance is analyzed under the developed zonotopic estimation method. A sufficient condition is further established to ensure the boundedness of the size of the obtained zonotope. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.