Probability of error in digital fiber optic systems with inter-symbol interference and signal dependent additive noise

Data transmission via optical fiber is a new discipline of communication theory. The principal difference from conventional baseband data transmission, which is characterized by a signal independent additive Gaussian noise, is the existence of a signal dependent shot noise.This paper presents a technique for estimating the error probability performance of digital systems with inter-symbol interference and signal dependent additive noise. For binary antipodal (±1) systems, the approximate upper bound to the error probability is twice the lower bound. Hence either can be taken as a good approximation to the actual error probability. The technique is then applied to a model of some promising optical data communication systems and a good approximation to the error probability is obtained. Some observations about the effect of various system parameters on the error probability and some numerical examples are presented.     

Output regulation control for stochastic systems with additive noise

This paper investigates the robust output regulation problem for stochastic systems with additive noises. As is known, for the output regulation control problem, a general method is to regard that the system is disturbed by an autonomous exosystem (which is consisted by external disturbances and reference signals), and for the system disturbed by the white noise, the stochastic differential equations (SDEs) should be utilized in modeling, accordingly, a controller with a feedforward regulator is constructed for the stochastic system with an exosystem, which can not only cancel the external disturbance, but also transform the trajectory tracking problem into the stabilization problem; In consideration of the state variables in stochastic systems cannot be measured completely, we embed an observer to the controller, such that the random interference can be suppressed, and the trajectory tracking can be achieved. Based on the stochastic control theory, the criteria of the exponential practical stability in the mean square is presented for the closed-loop system, finally, through tuning the controller parameters, the mean square of the tracking error can converge to an arbitrarily small neighborhood of the origin.     

Moving horizon estimation for ARMAX processes with additive output noise

Auto-Regressive-Moving-Average with eXogenous input (ARMAX) models play an important role in control engineering for describing practical systems. However, ARMAX models can be non-realistic in many practical contexts because they do not consider the measurement errors on the output of the process. Due to the auto-regressive nature of ARMAX processes, a measurement error may affect multiple data entries, making the estimation problem very challenging. This problem can be solved by enhancing the ARMAX model with additive error terms on the output, and this paper develops a moving horizon estimator for such an extended ARMAX model. In the proposed method, measurement errors are modeled as nuisance variables and estimated simultaneously with the states. Identifiability was achieved by regularizing the least-squares cost with the ?₂-norm of the nuisance variables, which leads to an optimization problem that has an analytical solution. For the proposed estimator, convergence results are established and unbiasedness properties are also proved. Insights on how to select the tuning parameter in the cost function are provided. Because of the explicit modeling of output noise, the impact of a measurement error on multiple data entries can be estimated and reduced. Examples are given to demonstrate the effectiveness of the proposed estimator in dealing with additive output noise as well as outliers.     

Non-parametric adaptive locally asymptotically optimum detection in additive noise

In this paper, a new approach to non-parametric signal detection with independent noise sampling is presented. The present approach is based on the locally asymptotically optimum (LAO) methodology, which is valid for vanishingly small signals and very large sample sizes, and on semi-parametric statistics. Its unique feature and essential difference from other techniques is that LAO non-parametric detectors are optimum according to the Neyman-Pearson criterion by being asymptotically uniformly most powerful at false alarm level α (AUMP (α)) and adaptive in the sense that no loss in Fisher's information number is incurred when the underlying noise process is no longer parametrically defined. Accordingly, they are robust against deviations from the postulated noise model and, unlike other non-parametric detectors, are distribution-free under both hypotheses H₀ (“noise only present”) and H₁ (“signal and noise present”). Non-parametric LAO detectors are derived from an asymptotic stochastic expansion of the log-likelihood ratio for coherent and narrowband incoherent “on-off” signals. Moreover, under the present framework it is shown that, in direct contrast to already known results, the non-parametric sign detector is AUMP (α) and adaptive even for non-constant signal samples.     

Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays

Recently, a polynomials-based integral inequality was proposed by extending the Moon’s inequality into a generic formulation. By imposing certain structures on the slack matrices of this integral inequality, this paper proposes an orthogonal-polynomials-based integral inequality which has lower computational burden than the polynomials-based integral inequality while maintaining the same conservatism. Further, this paper provides notes on relations among recent general integral inequalities constructed with arbitrary degree polynomials. In these notes, it is shown that the proposed integral inequality is superior to the Bessel–Legendre (B–L) inequality and the polynomials-based integral inequality in terms of the conservatism and computational burden, respectively. Moreover, the effectiveness of the proposed method is demonstrated by an illustrative example of stability analysis for systems with additive time-varying delays.     

The time-delay digital tanlock loop: performance analysis in additive Gaussian noise

Recently, a new non-uniform sampling digital phase-locked loop, the time-delay digital tanlock loop (TDTL), has been proposed. We have analyzed in a previous work the first- and second-order TDTLs under noise-free conditions. In this work, we analyze the performance of the TDTL in the presence of additive Gaussian noise for different values of the loop parameters. It is shown that the expected value of the steady-state phase errors at the input and the output of the phase error detector are equal to the noise-free steady-state values, while the variance is significantly reduced when the signal-to-noise ratio is increased or the phase shift introduced by the time-delay approaches 90°. The locking ranges of the TDTL parameters under noise-free conditions are unchanged by the presence of noise.     

On stabilization for systems with two additive time-varying input delays arising from networked control systems

This paper is concerned with the stability and stabilization for systems with two additive time-varying input delays arising from networked control systems. A new Lyapunov functional is constructed and a tighter upper bound of the derivative of the Lyapunov functional is derived by applying a convex polyhedron method. The resulting stability criteria are of fewer matrix variables and less conservative than some existing ones. Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Numerical examples are given to show the less conservatism of the stability criteria and the effectiveness of the designed method.     

Stochastic model predictive control for linear systems with unbounded additive uncertainties

This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form, which are treated in analogy with robust constraints, by using the probabilistic reachable set. The first one is the time-varying tube-based stochastic model predictive control algorithm, which is designed by employing the time-varying probabilistic reachable sets as tubes. The second one is the constant tube-based stochastic model predictive control algorithm, which is developed by enforcing a constant tightened constraint in the entire prediction horizon. In addition, the soft constraints are proposed to associate with the state initialization in the algorithms to enhance the feasibility. The algorithm feasibility and closed-loop stability results are provided. The efficacy of the approaches is demonstrated by means of numerical simulations.     

Incentive feedback Stackelberg strategy for stochastic systems with state-dependent noise

This paper designs an incentive strategy for a class of stochastic Stackelberg games in finite horizon and infinite horizon, respectively. The obtained incentive Stackelberg strategy works well in the sense that the leader will get his desired solution in the end. Different from the existing works, the state-dependent noise is considered in the design of the incentive Stackelberg strategy. Moreover, the mean-square stabilization can be guaranteed by the follower. The algorithm procedure is put forward to obtain effectively the incentive feedback Stackelberg strategy in infinite horizon. Finally, two examples are given to shed light on the effectiveness of the proposed algorithm procedure.     

Performance degradation due to measurement noise in control systems with disturbance observers and saturating actuators

Augmenting feedback control systems with disturbance observer (DOB) is a widely used technique in system design to compensate for the effect of exogenous disturbances as well as plant model uncertainties. In practice, actuator saturation should be taken into account in the design of control systems with DOB. In such cases, we have observed performance degradation due to zero mean measurement noise in the form of tracking loss. This phenomenon has never been reported in DOB literature. This paper reports the phenomenon, analyzes the conditions under which the tracking loss occurs, and also presents design guidelines to avoid the tracking loss. Experimental verification is also provided using a BLDC motor drive testbed.     

Mean-square consensus of hybrid multi-agent systems with noise and nonlinear terms over jointly connected topologies

This paper studies the mean-square consensus of second-order hybrid multi-agent systems over jointly connected topologies. Systems with time-varying delay and multiplicative noise are considered. The date sampling control technique is adopted. Through matrix transformation, a positive definite matrix transformed by the Laplacian matrix is obtained, where the Laplacian matrix is a connected subgraph divided by the jointly connected topologies. By using graph theory, matrix theory and Lyapunov stability theory, sufficient conditions and the upper bound of time delays for the mean-square consensus are obtained. Finally, several simulations are presented to demonstrate the validity of the control method.     

Stabilization and destabilization of nonlinear systems via intermittent stochastic noise with application to memristor-based system

This paper considers the stabilization and destabilization of a given nonlinear system by an intermittent Brownian noise perturbation. We give some distinct conditions and conclusions on almost sure exponential stability and instability, which are related to the control period T and the noise width δ. These results are then exploited to examine stabilization and destabilization via intermittent stochastic perturbation and applied to the stabilization of a memristor-based chaotic system. Two numerical examples are presented to illustrate the theoretical results.     

An iterative state-space identification method with data correlation for MIMO systems with measurement noise

This work presents an iterative concept of the State-space Realization Algorithm with Data Correlation (SSRA-DC) to identify MIMO systems with measurement noise and subjected to a reduced number of samples acquired from the process. The measurement noise is characterized as a random signal with properties of white noise and having up to 1% of the output signal amplitude. The proposed technique is based on the Markov parameters matrix’s feedback in an iterative algorithm supported by the SSRA-DC method. A gain factor takes part in the closed-loop to update the Markov parameters matrix, reducing their residues at each iteration. A fixed value for the gain is applied all over the iterations. The Gaussian White Noise (GWN) is employed as the input excitation signal in simulated experiments of mass-damper-springer models with 50 and 100 degrees of freedom. For some algorithm settings, one hundred simulations, each holding more than 100 iterations, are performed to statistically demonstrate the iterative algorithm’s effectiveness compared to the conventional SSRA-DC. Further comparative analysis is accomplished between the iterative method with the ARMAX and N4SID algorithms.     

Filtering based parameter estimation for observer canonical state space systems with colored noise

This paper surveys the identification of observer canonical state space systems affected by colored noise. By means of the filtering technique, a filtering based recursive generalized extended least squares algorithm is proposed for enhancing the parameter identification accuracy. To ease the computational burden, the filtered regressive model is separated into two fictitious sub-models, and then a filtering based two-stage recursive generalized extended least squares algorithm is developed on the basis of the hierarchical identification. The stochastic martingale theory is applied to analyze the convergence of the proposed algorithms. An experimental example is provided to validate the proposed algorithms.     

Parameter identification of time-delayed nonlinear systems: An integrated method with adaptive noise correction

This paper proposes a novel method called the adaptive-noise-correction integrated parameter identification (ANCPI) for time-delayed nonlinear systems. Compared with the existing de-noising techniques, the significance of the proposed method is the use of the system itself to correct the noise-polluted components so that the accuracy of parameter identification is enhanced. To achieve the goal of adaptive noise correction, this study starts from the case of periodic response and then parameterizes the noise correction as the coefficient correction of harmonic basis. In this way, the parameter identification integrated with noise correction can be performed as the parameter optimization of the error function. For the convenience of application, a user-friendly program package is further provided and a detailed tutorial is presented in the supplementary material.     

Development of time-limited model reduction technique for one-dimensional and two-dimensional systems with error bound via balanced structure

In this article, the two-dimensional model is decomposed into two one-dimensional models using the minimal rank-decomposition condition, and the model reduction is conducted on these two one-dimensional models using time-limited Gramians. The proposed framework works for both one-dimensional and two-dimensional systems. The suggested approach addresses the primary flaw in Gawronski & Juang’s problem of reduced-order model instability. Researchers revealed some stability preservation solutions to address this key flaw, which ensure the stability of one-dimensional reduced-order systems; nevertheless, these strategies result in large approximation errors. However, to the best of the authors’ knowledge, there is no literature available for the stability preserving time-limited-intervals Gramians based model reduction framework for the two-dimensional discrete-time systems. In comparison to other stability-preserving strategies, the proposed framework provides an a priori error-bound formulation that is easily computable. The simulation results show that the proposed framework performs well compared to other existing stability-preserving methods, demonstrating its usefulness.     

Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed

In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated. First of all, by using integral-type error function and twice zeroing neural network (or termed, Zhang neural network) formula, as the preliminaries and bases of future problems solving, two continuous-time advanced zeroing neural network models are presented for solving continuous time-variant equation systems. Secondly, a one-step-ahead numerical differentiation rule termed 5-instant discretization formula is presented for the first-order derivative approximation with higher computational precision. By exploiting the presented 5-instant discretization formula to discretize the continuous-time advanced zeroing neural network models, two novel discrete-time advanced zeroing neural network models are proposed. Theoretical analyses on the convergence and precision of the discrete-time advanced zeroing neural network models are proposed. In addition, in the presence of disturbance, the proposed discrete-time advanced zeroing neural network models still possess excellent performance. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed discrete-time advanced zeroing neural network models for solving the future equation systems.     

Order reduction of linear systems using an error minimization technique

A simple method is proposed for order reduction of linear continuous systems with real distinct eigenvalues. The steady state parts of the unit step responses of the original and reduced-order models are matched in this method. Zeros are synthesized by minimizing the error between the transient responses, where as dominant poles are retained. An example is solved to illustrate the superiority of the method over some existing ones.