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In this article, the zonotopic distributed fusion estimation problem is investigated for a class of general nonlinear systems over binary sensor networks subject to unknown-but-bounded (UBB) noises. The network communication from nodes to the fusion center is confined to the limited bit rate. To alleviate the impact from less measurement information of the binary sensor, a modified innovation is constructed to improve the estimation accuracy. Then, a novel coding-decoding approach is proposed to ensure that the decoder has the ability to decode information from each node. Based on the matrix weighting fusion method, a distributed fusion algorithm is put forward under the zonotopic set-membership filtering framework, and the F -radius of the local zonotopic sets are derived and minimized by selecting the filtering gain parameters. Moreover, the bit rate allocation scheme and the weighting coefficients are determined by resolving two optimization problems. In addition, a sufficient condition is established to guarantee the uniform boundedness of the F -radius of the fused zonopotic. Finally, the ballistic object tracking systems is utilized to illustrate the availability of the presented algorithm.
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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.
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A distributed H∞ filtering issue is addressed in this paper for discrete-time nonlinear systems in the face of replay attacks over sensor networks, where an indicator variable is introduced to describe whether a replay attack is launched by the adversaries. First, an interesting pattern dependent on three parameters including a time-varying one is established to account for the temporal behavior of malicious attacks. Then, taking advantage of such a model, the resulting filter dynamic is transformed into a switching system with a subsystem with time-varying delays. By means of the famous switching system theory, a sufficient condition guaranteeing the H∞ performance is derived to disclose the tolerant attack condition, that is, the attack-active duration and proportion. In addition, the applicable filter gains are achieved with the aid of the solutions of matrix inequalities. Finally, an example is purposively given to adequately illustrate the availability of the developed secure filtering strategy.
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This article is concerned with the distributed state estimation problem over wireless sensor networks (WSNs), where each smart sensor is capable of harvesting energy from the external environment with a certain probability. The data transmission between neighboring nodes is dependent on the energy level of each sensor, and the internode communication is deemed as a failure when the current energy level is inadequate to guarantee the normal data transmission. Considering the intermittent information exchange over WSNs, a novel distributed state estimator is first constructed via introducing a set of indicator functions, and then the evolution of the probability distribution of energy level and its steady-state distribution is systematically discussed by resorting to the eigenvalue analysis approach and the mathematical induction. Furthermore, the optimal estimator gain is derived by minimizing the trace of the estimation error covariance under known communication sequences. In addition, the convergence of the minimized upper bound of the expected estimation error covariance is analyzed under any initial condition. Finally, an illustrative example regarding the target tracking problem is provided to verify the validity of the obtained theoretical results.
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This article is concerned with supplementary control of discrete-time nonlinear systems with multiple controllers in the framework of goal representation heuristic dynamic programming (GrHDP), where a logarithmic quantizer is used to govern the network communication. For the addressed problem, a neural network (NN)-based observer is first proposed to estimate the unknown system state in the simultaneous presence of quantized influence. In light of the estimated states and the ideal control inputs via a zero-sum game, a GrHDP algorithm with a reinforced term is developed to implement the supplementary control task, where some novel weight updating rules are constructed by virtue of an additional tunable parameter to improve the system performance. Furthermore, a set of conditions about the stability of estimated error dynamics of both observer states and updated NNs' weights are derived by resorting to the Lyapunov stability theory. Finally, the effectiveness of the developed method is verified by a power system and a numerical experiment.
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The paper investigates secure filtering of nonlinear large-scale systems suffering from randomly occurring DoS attacks. By introducing an adjustable parameter, an adaptive event-triggering mechanism is proposed for the sake of decreasing the transmission burden of signals, where the memory is utilized to reflect the influence of past triggered information. The main objective is to design an event-based secure filter to ensure that the dynamics of filtering errors is input-to-state stable in the mean square. Using the constructed Lyapunov function, a sufficient condition is derived where some element matrix inequalities are utilized to handle the inherent coupling of subsystems. Furthermore, the desired filter gains are parameterized by resorting to the feasibility of matrix inequalities. Finally, a numerical simulation about a power system is provided to verify the effectiveness of the developed secure filtering algorithm.
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This article focuses on the distributed maximum correntropy filtering issue for general stochastic nonlinear systems subject to deception attacks. The considered nonlinear functions consist of a determined one and a stochastic one, and the stochastic signals sent by deception attacks with identified statistic characteristics could be non-Gaussian. The corresponding calculation formulas of both the filter gains and the upper bound of the filter error covariance are proposed by means of the Taylor series expansion and the fixed-point iterative update rule, where the weighted maximum correntropy criterion is utilized to take the place of traditional minimum covariance indexes. Such an upper bound is only dependent on the local information, neighbor information, and the identified statistics of deception attacks and, therefore, the developed filtering scheme realizes the requirement of distributed calculation. Furthermore, a simplified version is obtained by removing weights in the correntropy criterion. Finally, an illustrative example is given to verify the effectiveness of developed distributed maximum correntropy filtering subject to deception attacks.
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This article focuses on the finite-horizon H∞ bipartite consensus control problem for a class of discrete time-varying cooperation-competition multiagent systems (DTV-CCMASs) with the round-robin (RR) protocol. The cooperation-competition relationship among agents is characterized by a signed graph, whose edges are with positive or negative connection weights. Specifically, a positive weight corresponds to an allied relationship between two agents and a negative one means an adversary relationship. The data exchange between each agent and its neighbors is orchestrated by an RR protocol, where only one neighboring agent is authorized to transmit the data packet at each time instant, and therefore, the data collision is prevented. This article aims to design a bipartite consensus controller for DTV-CCMASs with the RR protocol such that the predetermined H∞ bipartite consensus is satisfied over a given finite horizon. A sufficient condition is first established to guarantee the desired H∞ bipartite consensus by resorting to the completing square method. With the help of an auxiliary cost combined with the Moore-Penrose pseudoinverse method, a design scheme of the bipartite consensus controller is obtained by solving two coupled backward recursive Riccati difference equations (BRRDEs). Finally, a simulation example is given to verify the effectiveness of the proposed scheme of the bipartite consensus controller.
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In this paper, the neural-network (NN)-based consensus control problem is investigated for a class of discrete-time nonlinear multiagent systems (MASs) with a leader subject to input constraints. Relative measurements related to local tracking errors are collected via some smart sensors. A local nonquadratic cost function is first introduced to evaluate the control performance with input constraints. Then, in view of the relative measurements, an NN-based observer under the event-triggered mechanism is designed to reconstruct the dynamics of the local tracking errors, where the adopted event-triggered condition has a time-dependent threshold and the weight of NNs is updated via a new adaptive tuning law catering to the employed event-triggered mechanism. Furthermore, an ideal control policy is developed for the addressed consensus control problem while minimizing the prescribed local nonquadratic cost function. Moreover, an actor-critic NN scheme with online learning is employed to realize the obtained control policy, where the critic NN is a three-layer structure with powerful approximation capability. Through extensive mathematical analysis, the consensus condition is established for the underlying MAS, and the boundedness of the estimated errors is proven for actor and critic NN weights. In addition, the effect from the adopted event-triggered mechanism on the local cost is thoroughly discussed, and the upper bound of the corresponding increment is derived in comparison with time-triggered cases. Finally, a simulation example is utilized to illustrate the usefulness of the proposed controller design scheme.
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This paper investigates the finite-horizon H∞ containment control issue for a general discrete time-varying linear multiagent systems with multileaders. All followers in such a system are driven into a convex hull spanned by multiple leaders, which can be transformed into a problem of tracking a virtual trajectory generated by these leaders. For this purpose, a local state observer is put forward to estimate the state of each agent itself. Then, the estimated state is transmitted to corresponding neighbors governing by an innovation-based event-triggered scheduling protocol. The purpose of the addressed problem is to design both an event-based distributed controller and a state observer such that a prescribed H∞ containment index can be achieved over a given finite horizon. First, with the help of the completing the square method, a sufficient condition is established to ensure the desired H∞ containment performance. Then, by resort to a novel nominal energy cost index combined with Moore-Penrose pseudoinverse method, the desired controller and observer parameters are obtained by solving two coupled backward recursive Riccati difference equations. Two positive scalars in proposed nominal energy cost index provide a tradeoff among the controlled tracking errors, the energy of transformed control inputs, and the precision of estimated states. Finally, a simulation example is given to illustrate the usefulness of the proposed theoretical results.
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An event-triggered distributed state estimation problem is investigated for a class of discrete-time nonlinear stochastic systems with unknown parameters over sensor networks (SNs) subject to switched topologies. An event-triggered communication strategy is employed to govern the information broadcast and reduce the unnecessary resource consumption. Based on the adopted communication strategy, a distributed state estimator is designed to estimate the plant states and also identify the unknown parameters. In the framework of input-to-state stability, sufficient conditions with an average dwell time are established to ensure the boundedness of estimation errors in mean-square sense. In addition, the gains of the designed estimators are dependent on the solution of a set of matrix inequalities whose dimensions are unrelated to the scale of underlying SNs, thereby fulfill the scalability requirement. Finally, an illustrative simulation is utilized to verify the feasibility of the proposed design scheme.
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The neural-network (NN)-based output-feedback control is considered for a class of stochastic nonlinear systems under round-Robin (RR) scheduling protocols. For the purpose of effectively mitigating data congestions and saving energies, the RR protocols are implemented and the resulting nonlinear systems become the so-called protocol-induced periodic ones. Taking such a periodic characteristic into account, an NN-based observer is first proposed to reconstruct the system states where a novel adaptive tuning law on NN weights is adopted to cater to the requirement of performance analysis. In addition, with the established boundedness of the periodic systems in the mean-square sense, the desired observer gain is obtained by solving a set of matrix inequalities. Then, an actor-critic NN scheme with a time-varying step length in adaptive law is developed to handle the considered control problem with terminal constraints over finite-horizon. Some sufficient conditions are derived to guarantee the boundedness of estimation errors of critic and actor NN weights. In view of these conditions, some key parameters in adaptive tuning laws are easily determined via elementary algebraic operations. Furthermore, the stability in the mean-square sense is investigated for the discussed issue in infinite horizon. Finally, a simulation example is utilized to illustrate the applicability of the proposed control scheme.
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In this brief, we study the detectability issues in the context of distributed state estimation problems for a class of locally undetectable sensor networks. First, we introduce a novel detectability condition, i.e., weightedly uniform detectability (WUD), which is a sufficient condition to prove that the error covariances of the consensus filtering are uniformly bounded even though the local sensor nodes are undetectable. Different from the existing detectability (or observability) conditions, our condition includes the interacting weights which could further optimize the lower detectability Gramian bound. Hence, a new weights selection method is derived in term of the criterion of WUD. This new rule of selecting weights provides a new framework for distributed state estimation. The advantages of this approach lead to a better performance in estimation without extra computational burden to the filtering process. Finally, an example shows the effectiveness of the proposed method.
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In this paper, the H∞ fuzzy filtering problem is investigated for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with randomly occurring uncertainties and randomly occurring interval time-varying delays, as well as channel fadings. A sequence of random variables obeying the Bernoulli distribution is utilized to govern the randomly occurring uncertainties and probabilistic interval time-varying delays. Simultaneously, the Rice fading model is employed to describe the phenomena of channel fadings by setting different values of the channel coefficients. Our attention is focused on the design of an H∞ fuzzy filter such that the filtering error dynamics is exponentially mean-square stable and the disturbance rejection attenuation is constrained to a given level by means of the H∞-performance index. In the presence of the randomly occurring phenomena, sufficient conditions are derived, via stochastic analysis and Lyapunov functional approach, for the existence of desired filter ensuring both the exponential mean-square stability and the prescribed H∞ performance. The filter parameters can be obtained by solving a convex optimization problem via the semidefinite program method. Finally, a numerical example is utilized to illustrate the usefulness and effectiveness of the proposed design technique.
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In this paper, the H∞ state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements. With the aid of the interval matrix approach, we make the first attempt to characterize the uncertainties entering into the inner coupling matrix. The incomplete measurements under consideration include sensor saturations, quantization, and missing measurements, all of which are assumed to occur randomly. By introducing a stochastic Kronecker delta function, these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability. With the measurement model, a set of H∞ state estimators is designed such that, for all admissible incomplete measurements as well as the uncertain coupling strength, the estimation error dynamics is exponentially mean-square stable and the H∞ performance requirement is satisfied. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method. Finally, a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.
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In this paper, the state estimation problem is investigated for a class of discrete time-delay nonlinear complex networks with randomly occurring phenomena from sensor measurements. The randomly occurring phenomena include randomly occurring sensor saturations (ROSSs) and randomly varying sensor delays (RVSDs) that result typically from networked environments. A novel sensor model is proposed to describe the ROSSs and the RVSDs within a unified framework via two sets of Bernoulli-distributed white sequences with known conditional probabilities. Rather than employing the commonly used Lipschitz-type function, a more general sector-like nonlinear function is used to describe the nonlinearities existing in the network. The purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that, for all probabilistic sensor saturations and sensor delays, the dynamics of the estimation error is guaranteed to be exponentially mean-square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an H∞-norm. In terms of a novel Lyapunov-Krasovskii functional and the Kronecker product, sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method. A simulation example is provided to show the usefulness of the proposed state estimation conditions.