Dependent Noises Research Articles

Static output feedback H2/H∞ control with spectrum constraints for stochastic systems subject to multiplicative noises

ABSTRACTThis paper investigates the problem of static output feedback control with spectrum constraints for linear continuous-time stochastic systems with state dependent noises. By using the spectrum technique, the notion of stability for continuous-time stochastic systems is proposed. Subsequently, the design method of the static output feedback controller is presented by solving a set of linear matrix inequalities. Under stability, a sufficient condition for the existence of stochastic control is derived, which transforms the problem of control into a convex optimization problem. Finally, a numerical example is given to show the effectiveness of the obtained results.

Analysis of nonlinear state space model with dependent measurement noises

ABSTRACTThis paper presents a nonlinear state space model with considering a first-order autoregressive model for measurement noises. A recursive method using Taylor series based approximations for filtering, prediction and smoothing problem of hidden states from the noisy observations is designed. Also, an expectation-maximization algorithm for calculating the maximum likelihood estimators of parameters is presented. The closed form solutions are obtained for estimating of the hidden states and the unknown parameters. Finally, the performance of the designed methods are verified in a simulation study.

Event-based H∞ fault estimation for networked time-varying systems with randomly occurring nonlinearities and (x, v)-dependent noises

In this paper, the problem of finite-horizon H∞ fault estimation is investigated for a class of networked time-varying stochastic systems with randomly occurring nonlinearities and state- and disturbance-dependent noises (also called (x, v)-dependent noises). An event-triggered scheme is proposed to reduce data transmission burden where the current measurement is transmitted only when the certain condition is satisfied. The aim of the addressed problem is to design a fault estimator, in the presence of randomly occurring nonlinearities and (x, v)-dependent noises, such that faults can be estimated through measurement outputs. By employing the stochastic analysis method, the sufficient conditions are derived to guarantee that the error dynamics of estimations satisfies a prescribed H∞ performance constraint. Moreover, the parameters of fault estimator can be calculated via the recursive linear matrix inequality (RLMI) approach. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

Output-feedback [formula omitted] consensus control for stochastic time-varying multi-agent systems with [formula omitted]-dependent noises

In this paper, the output feedback H2∕H∞ consensus control problem is investigated for discrete time-varying stochastic multi-agent systems with state, control and disturbance-dependent noises (also called (x,u,v)-dependent noises). Two new concepts for the H2 and H∞ consensus requirements are proposed to quantify the transient behavior of the consensus, over a finite horizon, for the addressed time-varying multi-agent systems. We aim to design an output feedback consensus controller such that the closed-loop multi-agent systems achieve the prescribed H2 and H∞ consensus performances over a finite horizon. By using the completing squares method and stochastic analysis techniques, sufficient conditions are derived for the existence of the desired output-feedback H2∕H∞ consensus controller in terms of the solution to two coupled backward recursive Riccati difference equations (RDEs). Moreover, an iterative algorithm is proposed for solving the RDEs by resorting to the Moore–Penrose pseudo inverse. A numerical example is utilized to illustrate the effectiveness of the proposed H2∕H∞ consensus control strategy.

Event-based fault detection for T–S fuzzy systems with packet dropouts and (x, v)-dependent noises

This paper deals with the event-based fault detection problem for T–S fuzzy systems with packet dropouts as well as state- and disturbance-dependent noises ((x, v)-dependent noises for short). To utilize limited network resources efficiently, the event-triggered mechanism is employed such that only selected valuable data is transmitted to the filter according to whether specific events happen or not. The aim of the addressed problem is to design a fuzzy fault detection filter which guarantees the stochastic stability of the overall fault detection dynamics as well as the robustness against disturbances and sensitivity to faults of the residual signal. Some sufficient criteria are obtained for the existence of the desired fault detection filter which can be designed by solving a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the validity of the derived results.

Delay-distribution-dependent [formula omitted] state estimation for delayed neural networks with [formula omitted]-dependent noises and fading channels

This paper deals with the H∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results.

Event-Based $H_\infty $ State Estimation for Time-Varying Stochastic Dynamical Networks With State- and Disturbance-Dependent Noises.

In this paper, the event-based finite-horizon H∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v) -dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.

Linear quadratic regulation for discrete‐time systems with multiplicative noise and multiple input delays

SummaryThis paper is concerned with the optimal linear quadratic regulation problem for discrete‐time systems with state and control dependent noises and multiple delays in the input. We show that the problem admits a unique solution if and only if a sequence of matrices, which are determined by coupled difference equations developed in this paper, are positive definite. Under this condition, the optimal feedback controller and the optimal cost are presented via some coupled difference equations. Our approach is based on the stochastic maximum principle. The key technique is to establish relations between the costate and the state. Copyright © 2016 John Wiley & Sons, Ltd.

Output-Feedback Control for Nonlinear Stochastic Systems With Successive Packet Dropouts and Uniform Quantization Effects

In this paper, the dynamic output-feedback control problem is studied for a class of discrete-time nonlinear stochastic systems with successive packet dropouts and uniform quantization effects. The stochastic system under investigation involves state-, control-, and disturbance-dependent noises (also called ( ${x}$ , ${u}$ , ${v}$ )-dependent noises) that bring in substantial difficulties in the stability analysis. The phenomenon of successive packet dropouts is governed by a binary switching random sequence. The measurement output is subject to the uniform quantization which results in the norm-bounded disturbances, and the concept of input-to-state stability in probability is introduced to deal with this kind of disturbances. In virtue of intensive stochastic analysis, several sufficient conditions are established to guarantee that the closed-loop system is input-to-state stable in probability under the effects of probabilistic packet dropouts as well as uniform quantizations. As an easy consequence, the design problem with linear output-feedback controllers is discussed for the benefits of practical applications and some simplified conditions are derived. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

Robust H 2 / H ∞ control for periodic stochastic difference systems with mutiplicative noise

The aim of this study is to investigate the discrete-time periodic stochastic mixed H 2/H ∞ control problem with state and external disturbance dependent noises. Under the assumption of 𝒦 N -exact observability, the authors present a sufficient condition for the existence of mixed H 2/H ∞ control for stochastic periodic difference systems, which transforms the H 2/H ∞ controller design into solving four coupled matrix-valued equations.

PN Code Acquisition in Multiplicative and Weakly Dependent Non-Gaussian Noises based on Locally Optimum Detection Statistic

In most previously reported studies on pseudonoise (PN) code acquisition, independent additive noises have been assumed in various noise environments. The use of an independent observation model may cause considerable performance degradation in modern high datarate communication systems. In these studies, only additive noise model is considered. In this paper, a new detector for PN code acquisition in multiplicative and weakly dependent nonGaussian noises is proposed. Modeling the acquisition problem as a hypothesis testing problem, the test statistical is derived for multiplicative and weakly dependent non-Gaussian noises, based on the locally optimum detection technique. Numerical results show that the proposed detector can offer substantial performance improvement over the conventional schemes in multiplicative and weakly dependent non-Gaussian noises.

Sensor selection for nonlinear systems in large sensor networks

In this paper, we consider multistage look-ahead sensor selection problems for nonlinear dynamic systems such as radar target tracking systems. We investigate the problem for large sensor networks for both independent and dependent Gaussian measurement noises in the presence of temporally separable as well as inseparable constraints, e.g., energy constraints. First, when the measurement noises are uncorrelated between sensors, we derive the optimal solution for sensor selection when the constraints are temporally separable. When constraints are temporally inseparable, we can obtain near-optimal solutions by relaxing the nonconvex problem formulation to a linear programming problem so that the sensor selection problem for a large sensor network can be solved in a computationally efficient manner. For illustration, a radar target tracking problem is considered where it is shown that the new method presented for nonlinear dynamic systems performs better than the method based on linearizing the nonlinear equations and using previous sensor selection methods for large sensor networks. Finally, when the measurement noises are correlated between the sensors, the sensor selection problem with temporally inseparable constraints can be relaxed to a Boolean quadratic programming problem,,which can be efficiently solved by a Gaussian randomization procedure along with solving a semidefinite programming problem. Numerical examples show that the proposed method that includes consideration of dependence performs much better than the method that ignores dependence of noises.

Effect of Nonlinear Phase Noise on the Performance of $M$-Ary PSK Signals in Optical Fiber Links

The effects of amplified spontaneous emission (ASE) noise and nonlinear phase (NLP) noise on the symbol error rate performance of M-ary coherent phase shift keying (CPSK) and differential phase shift keying (DPSK) are analyzed. Expressions for the symbol error probability (SEP) are derived for the two cases of independent ASE and NLP noises and dependent ASE and NLP noises. Numerical results are presented for 2-, 4-, 8-, and 16-level signaling to demonstrate the applicability of the SEP expressions. Our results indicate that the SEPs for DPSK for the two cases are approximately the same except for M=2. The SEPs for CPSK differ significantly for the two cases for all M , implying that independent phase noise assumption is not valid for CPSK.

Infinite horizon $$H_2/H_\infty $$ optimal control for discrete-time Markov jump systems with ( $$x,u,v$$ )-dependent noise

In this paper, an infinite horizon $$H_2/H_\infty $$ control problem is addressed for a broad class of discrete-time Markov jump systems with ( $$x,u,v$$ )-dependent noises. First of all, under the...

A New Framework for Distributed Detection With Conditionally Dependent Observations

Distributed detection with conditionally dependent observations is known to be a challenging problem in decentralized inference. This paper attempts to make progress on this problem by proposing a new framework for distributed detection that builds on a hierarchical conditional independence model. Through the introduction of a hidden variable that induces conditional independence among the sensor observations, the proposed model unifies distributed detection with dependent or independent observations. This new framework allows us to identify several classes of distributed detection problems with dependent observations whose optimal decision rules resemble the ones for the independent case. The new framework induces a decoupling effect on the forms of the optimal local decision rules for these problems, much in the same way as the conditionally independent case. This is in sharp contrast to the general dependent case where the coupling of the forms of local sensor decision rules often renders the problem intractable. Such decoupling enables the use of, for example, the person-by-person optimization approach to find optimal local decision rules. Two classical examples in distributed detection with dependent observations are reexamined under this new framework: detection of a deterministic signal in dependent noises and detection of a random signal in independent noises.

Particle Filtering With Dependent Noise Processes

Modeling physical systems often leads to discrete time state-space models with dependent process and measurement noises. For linear Gaussian models, the Kalman filter handles this case, as is well described in literature. However, for nonlinear or non-Gaussian models, the particle filter as described in literature provides a general solution only for the case of independent noise. Here, we present an extended theory of the particle filter for dependent noises with the following key contributions: i) The optimal proposal distribution is derived; ii) the special case of Gaussian noise in nonlinear models is treated in detail, leading to a concrete algorithm that is as easy to implement as the corresponding Kalman filter; iii) the marginalized (Rao-Blackwellized) particle filter, handling linear Gaussian substructures in the model in an efficient way, is extended to dependent noise; and, finally, iv) the parameters of a joint Gaussian distribution of the noise processes are estimated jointly with the state in a recursive way.

State Observability and Observers of Linear-Time-Invariant Systems Under Irregular Sampling and Sensor Limitations

State observability and observer designs are investigated for linear-time-invariant systems in continuous time when the outputs are measured only at a set of irregular sampling time sequences. The problem is primarily motivated by systems with limited sensor information in which sensor switching generates irregular sampling sequences. State observability may be lost and the traditional observers may fail in general, even if the system has a full-rank observability matrix. It demonstrates that if the original system is observable, the irregularly sampled system will be observable if the sampling density is higher than some critical frequency, independent of the actual time sequences. This result extends Shannon's sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences. State observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises. Persistent excitation conditions are validated by designing sampling time sequences. By generating suitable switching time sequences, the designed state observers are shown to be convergent in mean square, with probability one, and with exponential convergence rates. Schemes for generating desired sampling sequences are summarized.

Adaptively Robust Phase Lock Loop for Low C/N Carrier Tracking in a GPS Software Receiver

An important issue in GPS applications is how to track GPS (global positioning system) signal precisely and continuously under low carrier-to-noise ratio (C/N). In this paper, an adaptively robust filter based low C/N carrier phase lock loop (PLL) is developed under a GPS software receiver platform. Considering the effect of low C/N carrier signal on the traditional tracking loop, a parallel correlation tracking loop is established. A linear optimal estimator is designed to deal with the dependent noises in kinematics model and measurements. Furthermore, an adaptively robust filter is designed based on a three segment function adjust factor. When received signals are under favorable conditions, the performance of the new filter is very similar to a standard Kalman filter. For a practical weak carrier tracking, this new enhanced PLL intelligently tunes the loop parameters according to the total phase jitter analysis. It successfully resists the outliers and dynamic model errors by adaptively balancing the influence of updated dynamic model state and the measurements. The robustness and efficiency of the new filter is demonstrated by some real data testing experiments. The results verify that the standard deviation of the phase errors with this adaptively robust phase tracking loop can reach 0.01 cycles with satellite C/N ratios around 24 dB-Hz, which improves the performance significantly.

Asymptotic properties of MLE for partially observed fractional diffusion system with dependent noises

The paper studies long time asymptotic properties of the maximum likelihood estimator (MLE) for the signal drift parameter in a partially observed fractional diffusion system with dependent noise. Using the method of weak convergence of likelihoods due to Ibragimov and Khasminskii [1981. Statistics of Random Processes. Springer, New-York], consistency, asymptotic normality and convergence of the moments are established for MLE. The proof is based on Laplace transform computations which was introduced in Brouste and Kleptsyna [2008. Asymptotic properties of MLE for partially observed fractional diffusion system, preprint].

Discrete-time Indefinite LQ Control with State and Control Dependent Noises

This paper deals with the discrete-time stochastic LQ problem involving state and control dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. In this general setting, it is shown that the well-posedness and the attainability of the LQ problem are equivalent. Moreover, a generalized difference Riccati equation is introduced and it is proved that its solvability is necessary and sufficient for the existence of an optimal control which can be either of state feedback or open-loop form. Furthermore, the set of all optimal controls is identified in terms of the solution to the proposed difference Riccati equation.