Recursive state estimation for discrete time-varying stochastic nonlinear systems with randomly occurring deception attacks

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This paper deals with the consensus control problem for a class of discrete time-varying stochastic multi-agent systems with stochastic nonlinearities and deception attacks. A novel definition of quasi-consensus is proposed to reflect the consensus process where, at each time instant, all the agents are constrained to stay within a certain ellipsoidal region. The measurement output available for the controller is not only from the individual agent itself but also from its neighboring ones according to the given topology. A new deception attack model is proposed, where the attack signals are injected by the adversary to the measurement data during the process of information transmission via the communication network. By using a set of recursive matrix inequalities, sufficient conditions are derived for the existence of the desired control scheme for achieving the quasi-consensus. Subsequently, an optimization problem is formulated to seek the locally best consensus performance.

Multi-model information fusion Kalman filtering and white noise deconvolution

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic parameter systems with error variance constraints over a sensor network where the sensor outputs are subject to successive missing measurements. The phenomenon of the successive missing measurements for each sensor is modeled via a sequence of mutually independent random variables obeying the Bernoulli binary distribution law. To reduce the frequency of unnecessary data transmission and alleviate the communication burden, an event-triggered mechanism is introduced for the sensor node such that only some vitally important data is transmitted to its neighboring sensors when specific events occur. The objective of the problem addressed is to design a time-varying filter such that both the requirements and the variance constraints are guaranteed over a given finite-horizon against the random parameter matrices, successive missing measurements, and stochastic noises. By recurring to stochastic analysis techniques, sufficient conditions are established to ensure the existence of the time-varying filters whose gain matrices are then explicitly characterized in term of the solutions to a series of recursive matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of the developed event-triggered distributed filter design strategy.

National Natural Science Foundation of China under Grant 62003083, Grant 61873059, Grant 61873148, Grant 61922024 and Grang 61933007; Shanghai Science and Technology Program of China under Grant 20JC1414500; Shanghai Sailing Program of China under Grant 19YF1402400; Program of Shanghai Academic/Technology Research Leader of China under Grant 20XD1420100.

ABSTRACTThe objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, -exact detectability (resp. -exact detectability, -exact detectability, -exact detectability) and -exact observability (resp. -exact detectability, -exact detectability, -exact detectability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalised Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, -exact observability and -exact detectability, respectively.

This paper investigated the problem of state and fault estimation for nonlinear discrete time systems in presence of unknown disturbances. A novel unbiased minimum variance filter (UMVF) is derived by reconstructing the non linear version of NUMV filter. In this work we assume that no prior knowledge about the dynamic of the disturbance and the fault are known. In this paper we considers that the fault affects both the system state and measurement equations, but the disturbance affects only the system state. The NUMV filter presented in this paper is an extension of the filter presented in [11]. The efficacy of the proposed filter is demonstrated by two simulation examples.

Design of the modified fractional central difference Kalman filters under stochastic colored noises

This paper is concerned with the finite-horizon H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> quantized control problem for a class of discrete time-varying nonlinear networked control systems with earliest deadline first (EDF) schedule. EDF schedule is employed in the channels both from sensor to controller and controller to actuator. Moreover, the measurement output signal and control signal are quantized by a logarithmic quantizer before they enter the controller and system, respectively. The main purpose of the problem addressed is to design a dynamical output-feedback controller such that the prespecified H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of the system is guaranteed over a given finite time-horizon. To this end, a sufficient condition is firstly established for the existence of the desired output-feedback controller. Then, the controller parameters are characterized by solving a recursive linear matrix inequality. Finally, a numerical example is given to illustrate the effectiveness of the proposed control approach.

One of the most important problems in the estimation theory is the one-step prediction. The goal of this problem is to determine the predictions of states in the next time step. This paper focuses on the one-step prediction for nonlinear dynamic systems. The system under investigation involves unknown inputs and the system noises are correlated. In this approach, using the Taylor series expansion for nonlinear functions, a new augmented state nonlinear predictor is proposed for discrete time-varying nonlinear systems. This predictor is obtained by solving a deterministic min-max optimization based on the regularized least squares problem. Moreover, to reduce the computational complexity of the prediction solution, using a nonlinear transformation, we propose a two-stage predictor including lower order estimators for states and unknown inputs. Finally, a frequency modulated signal model is considered to illustrate the effectiveness and performance of the proposed approaches in comparison with the existing estimation methods.

In this paper, the Kalman-type recursive filtering problem is investigated for a class of discrete-time stochastic non-linear systems subject to time-delays and randomly occurring deception attacks. The deception attack under consideration is assumed to be bounded and occur in a random way, which is characterized by using the Bernoulli distribution white sequences. The purpose of the problem addressed in this paper is to design the Kalman-type recursive filter such that for all admissible randomly occurring cyber attacks, time-delays, Gaussian noises, deterministic nonlinearities and stochastic nonlinearities, an upper bound of the filtering error covariance matrix can be obtained in terms of two Riccati-like difference equations. Subsequently, by minimizing such an upper bound, the optimized filter gain can be derived. Finally, a simulation example is proposed to illustrate the effectiveness of the proposed Kalman-type recursive filter design scheme.

In this paper, the distributed state estimation problem is investigated for a class of discrete time-varying nonlinear systems over sensor networks with sensor resolution, where a binary encoding scheme is employed to address bandwidth limitations. The measurement output is converted into a binary bit string, conveyed through a memoryless binary symmetric channel subject to a certain probability of bit flips, and then reconstructed by a decoder. The influence of both sensor resolution and binary encoding scheme on estimation accuracy is considered simultaneously, where a distributed recursive state estimation strategy over sensor networks is constructed. Subsequently, the estimator gain that minimizes the upper bound on the estimation error covariance is obtained by solving Riccati-like difference equations. Finally, the validity of the developed algorithm is displayed through a simulation example.

This paper studies complete stable and unstable periodic solutions for n-dimensional nonlinear discrete dynamical systems. The positive and negative iterative mappings of discrete systems are used to develop mapping structures of the stable and unstable periodic solutions. The complete bifurcation and stability analysis are presented for the stable and unstable periodic solutions which are based on the positive and negative mapping structures. A comprehensive investigation on the Henon map is carried out for a better understanding of complexity in nonlinear discrete systems. Given is the bifurcation scenario based on positive and negative mappings of the Henon map, and the analytical predictions of the corresponding periodic solutions are achieved. The corresponding eigenvalue analysis of the periodic solutions is presented. The Poincare mapping sections relative to the Neimark bifurcations of periodic solutions are presented. A parameter map for periodic and chaotic solutions is developed. The complete unstable and stable periodic solutions in nonlinear discrete systems are presented for the first time. The results presented in this paper provide a new idea for one to rethink the current existing theories.

Designing for a convergent adaptive Kalman filter (AKF) which can be used in time-varying stochastic linear systems is considered. A necessary condition which can guarantee the designed AKF is convergent is proposed and proved. This necessary condition can be satisfied by choosing appropriate gains. In fact, choosing the gains is just a procedure of designing a convergent AKF. The AKF designed by the above procedure is convergent and only correlative with coefficient matrices of the system. So, it adapts to deal with time-varying stochastic linear systems. At last, the findings in this paper are validated by some simulations.

An Optimal Sequential Decentralized Filter of Discrete-time Systems with Cross-Correlated Noises