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This paper studies the consensus tracking problem based on optimised backstepping technique for multiagent systems with power exponential functions and the privacy protection. Under the optimised backstepping technique, the controllers with power functions are designed by utilising the reinforcement learning strategy. Moreover, the synchronisation error converges to a predetermined region within a user-defined settling time by utilising a speed function. To ensure the safety of communication, the privacy protection is applied to multiagent systems, which effectively prevent information exposure. Based on Lyapunov stability theory, the tracking errors of the system with power exponential functions converge to a predetermined region, and a simulation example proves the feasibility of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper presents a series of structure-preserving model order reduction algorithms for K-power bilinear systems via Laguerre functions. The method first aims to rewritten the K-power bilinear system as a general bilinear system and calculate the approximate low-rank factors of the cross Gramian of the bilinear system by combining the idea of Laguerre functions expansion of the matrix exponential function. After that, the approximate balanced system of the K-power bilinear system is constructed by the corresponding projection transformation of each subsystem. In order to achieve the purpose of model order reduction, the states with smaller singular values are then truncated, so as to further obtain the reduced order model. For this approach, there is a disadvantage that unstable systems may be generated although the original one is stable. To alleviate the inadequacies of this approach, we have improved the model reduction procedure, which is based upon the dominant subspace projection method. In addition, we also carried out a correlation analysis on the stability of improved algorithms. Finally, numerical experiments are employed to substantiate the effectiveness of the presented algorithms. [ABSTRACT FROM AUTHOR]

The purpose of this paper is two-fold. First, the smoothness of the distributed consensus control (DCC) protocols of multi-agent systems (MAS) with inherent nonlinear dynamics is investigated. Different from the traditional consensus protocols where variable structure control is considered for robust control, a continuous DCC is presented to achieve consensus tracking without control chattering. Using certain types of exponential functions, it is shown that different smooth DCC schemes can be constructed to achieve asymptotic consensus tracking with smooth control input for MAS with connected directed/undirected and fixed/switched communication topologies. Second, the formation control problem of nonholonomic wheeled mobile robots (WMR) is solved via the continuous DCC. By converting the formation problem into consensus problem using the agents' kinematics, the formation speed-control problem in planar motion is formulated and solved. The translational and rotational speeds inputs to the WMR are computed using continuous distributed consensus protocols to reduce chattering in the control inputs of mobile robots. The distinctive feature of the proposed consensus and formation algorithms is the high tracking precision with smooth control input to agents' dynamics. In simulation studies, different numerical examples are illustrated to demonstrate the performance and effectiveness of the proposed DCC. [ABSTRACT FROM AUTHOR]

Employing a state-based Discrete Event System (DES) modelling framework, this paper proposes a new fault diagnosis approach called measurement limitation-based abstract DES diagnosis (MLAD), which attempts to reduce state space complexity of the diagnosis process while simultaneously preserving full diagnosability. The MLAD approach carefully applies a set of distinct measurement limitation operations on the state variables of the original DES model based on fault compartmentalisation to obtain separate behaviourally abstracted DES models and corresponding abstract diagnosers with far lower state spaces. The set of measurement limitation operations are so designed that although, any single abstract diagnoser may compromise diagnosability in seclusion, the additive combination of all diagnosers running in parallel always ensures complete diagnosability. Effective measurement limitation also ensures that the combined state space of the abstract diagnosers is much lower than that of the single full diagnoser that may be derived from the original DES model. As a case study, we have employed MLAD to incorporate failure diagnosability in a practical electronic fuel injection system. Evaluations on standard practical benchmarks show that MLAD achieves significant reduction in state space as compared to conventional monolithic full diagnosis approaches. [ABSTRACT FROM AUTHOR]

In this paper, mean square exponential input-to-state stability (exp-ISS) of stochastic memristive complex-valued neural networks (SMCVNNs) is investigated. By utilising Lyapunov functional and stochastic analysis theory, a sufficient criterion is derived to assure the mean square exp-ISS of the SMCVNNs. The obtained results not only generalise the previous works in the literature about real-valued neural networks as special cases, but also can be easily checked by parameters of system. Numerical simulations are given to show the effectiveness of our theoretical results. [ABSTRACT FROM PUBLISHER]

Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilising stochastic contraction theory to conclude on exponential convergence of the unscented Kalman–Bucy filter. The underlying process and measurement models of interest are Itô-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual–actual systems framework to establish deterministic contraction of the estimated expected mean of process values. Under mild conditions of bounded process noise, we extend the results on deterministic contraction to stochastic contraction of the estimated expected mean of the process state. It follows that for the regions of contraction, a result on convergence, and thereby incremental stability, is concluded for the unscented Kalman–Bucy filter. The theoretical concepts are illustrated in two case studies. [ABSTRACT FROM AUTHOR]

In this paper, we study the determination of the optimal lead time, reorder point and order quantity considering that the back-order probability of a demand made during a stock-out period depends on the interval from the moment in which the order is placed until the next replenishment. Two models are analysed for the specification of the back-order probability: exponential functions and piecewise constant functions. The distribution of the lead time demand is assumed to be Poisson. An algorithm for the determination of the optimal order quantity, reorder point and lead time is given. A numerical example is presented to illustrate the results. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of event-based fault detection (FD) filter design for interval type-2 fuzzy systems in a network environment. Firstly, by employing the properties of exponential function, a novel adaptive event-triggering mechanism (AETM) where the boundedness of threshold function is guaranteed and the size of threshold function is inversely proportional to the size of 2-norm of the sampled-output-error is proposed to dynamically adapt the variation of the system and to reduce the unnecessary information communication between the sensor and the filter. Secondly, in the framework of time-delay systems, the FD system with a networked filter and an AETM is modelled as an interval time-varying delayed system. Then, a sufficient condition to implement co-design of the parameters of filter and trigger is obtained by applying a simple Lyapunov–Krasovskii functionals, combined with recently developed Wirtinger-based integral inequality and reciprocally convex inequality, and utilising congruent transformation method. Thirdly, based on the obtained co-design condition, an optimisation algorithm subject to convex constraints for the tradeoffs between resource utilisation and H ∞ performance of the FD system is further developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this manuscript a new variable sampling plan based on the exponentially weighted moving average (EWMA) statistic is proposed assuming that the quality characteristic follows the normal distribution. The plans are proposed when the standard deviation of the normal distribution is known or unknown. The plan parameters for both cases are determined such that the given producer's risk and consumer's risk are satisfied. The proposed plan includes the ordinary variable single sampling plan as a special case and its advantage over the single sampling plan is discussed in terms of the sample size. Extensive tables are provided for industrial use. [ABSTRACT FROM AUTHOR]

In manufacturing industries, the lifetime of an item is usually characterised by a random variableXand considered to be satisfactory ifXexceeds a given lower lifetime limitL. The probability of a satisfactory item is then ηL:=P(X≥L), calledconforming rate. In industrial companies, however, thelifetime performance index, proposed by Montgomery and denoted byCL, is widely used as a process capability index instead of the conforming rate. Assuming a parametric model for the random variableX, we show that there is a connection between the conforming rate and the lifetime performance index. Consequently, the statistical inferences about ηLandCLare equivalent. Hence, we restrict ourselves to statistical inference forCLbased on generalised order statistics, which contains several ordered data models such as usual order statistics, progressively Type-II censored data and records. Various point and interval estimators for the parameterCLare obtained and optimal critical regions for the hypothesis testing problems concerningCLare proposed. Finally, two real data-sets on the lifetimes of insulating fluid and ball bearings, due to Nelson (1982) and Caroni (2002), respectively, and a simulated sample are analysed. [ABSTRACT FROM AUTHOR]

This article deals with the problem of delay-dependent state estimation for discrete-time neural networks with time-varying delay. Our objective is to design a state estimator for the neuron states through available output measurements such that the error state system is guaranteed to be globally exponentially stable. Based on the linear matrix inequality approach, a delay-dependent condition is developed for the existence of the desired state estimator via a novel Lyapunov functional. The obtained condition has less conservativeness than the existing ones, which is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

This article presents new exponential stability and stabilisation conditions for Takagi-Sugeno fuzzy time-varying delay systems. Based on an improved Lyapunov-Krasovskii functional, the exponential stability and stabilisation conditions are derived in terms of linear matrix inequalities, which allows one to compute simultaneously the two bounds that characterise the exponential stability rate of the solution. Finally, some numerical examples are given to illustrate the effectiveness of the proposed conditions. [ABSTRACT FROM AUTHOR]

The article presents closed form solutions for a class of matrix linear systems whose state variable is a matrix. The formulation evaluates the state response of the system in terms of the original system matrices. The proposed solutions naturally fit systems which are most described conveniently by matrix processes. Its formulation uses a compact notation referred to as double matrix exponential functions, which is an extension of normal matrix exponential function. It is a straightforward extension of the solutions for ordinary vector linear systems studied in the past several decades and will play an important role in the design of matrix linear systems using original system matrices. [ABSTRACT FROM AUTHOR]

This article considers a class of delayed bi-directional associative memory (BAM) neural networks with reaction diffusion terms and delays. We obtain some simple criteria ensuring the existence and uniqueness of the equilibrium and its global exponential stability by applying homeomorphism mapping, constructing a new Lyapunov functional and inequality techniques. These criteria are independent of delays and posses infinitely adjustable real parameters, which improve and extend some recent results [J. Cao and M. Dong, "Exponential stability of delayed bidirectional associative memory networks", Appl. Math. Comput., 135, pp. 105-112, 2003; J. Cao and L. Wang, "Exponential stability and periodic oscillatory solution in BAM networks with delays", IEEE Trans. Neural Networ., 13, pp. 457-463, 2002; Q. Song and J. Cao, "Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms", Chaos Soliton. Fract., 23, pp. 421-430, 2005.] and have an important instructional significance in the designs and applications of bidirectional associative memory neural networks. [ABSTRACT FROM AUTHOR]