In this paper, a performance enhancement scheme has been investigated for a class of stochastic nonlinear systems via set-point adjustment. Considering the practical industrial processes, the multi-layer systematic structure has been adopted to achieve the control design requirements subjected to random noise. The basic loop control is given by PID design while the parameters have been fixed after the design phase. Alternatively, we can consider that there exists an unadjustable loop control. Then, the additional loop is designed for performance enhancement in terms of the tracking accuracy. In particular, a novel approach has been presented to dynamically adjust the set-points using the estimated states of the systems through extended Kalman filter (EKF). Minimising the entropy criterion, the parameters of the set-point adjustment controller can be optimised which will enhance the performance of the entire closed-loop systems. Based upon the presented scheme, the stochastic stability analysis has been given to demonstrate that the closedloop tracking errors are bounded in probability one. To indicate the effectiveness of the presented control scheme, the numerical examples have been given and the simulation results imply that the designed systems are bounded and the tracking performance can be enhanced simultaneously. In summary, a new framework for system performance enhancement has been presented even if the loop control is unadjustable which forms the main contribution of this paper.

The development and research of an ultrasonic-based concrete structural health monitoring system encounters a variety of problems, such as demands of decreasing complexity, high accuracy, and extendable system output. Aiming at these requirements, a low-cost extendable system based on FPGA with adjustable system output has been designed, and the performance has been evaluated by different assessment parameters set in this paper. Besides the description of the designed system and the experiments in air medium, the residual similarity and Pearson correlation coefficients of experimental and theoretical data have been used to evaluate the submodules’ output. The output performance of the overall system is evaluated by the Pearson correlation coefficient, root-mean-square error (RMSE), and magnitude-squared coherence with 40 experimental data. The maximum, median, minimum, and mean values in three-parameter datasets are analyzed for discussing the working condition of the system. The experimental results show that the system works stably and reliably with tunable frequency and amplitude output.

This paper investigates the randomness assignment problem for a class of continuous-time stochastic nonlinear systems, where variance and entropy are employed to describe the investigated systems. In particular, the system model is formulated by a stochastic differential equation. Due to the nonlinearities of the systems, the probability density functions of the system state and system output cannot be characterised as Gaussian even if the system is subjected to Brownian motion. To deal with the non-Gaussian randomness, we present a novel backstepping-based design approach to convert the stochastic nonlinear system to a linear stochastic process, thus the variance and entropy of the system variables can be formulated analytically by the solving Fokker–Planck–Kolmogorov equation. In this way, the design parameter of the backstepping procedure can be then obtained to achieve the variance and entropy assignment. In addition, the stability of the proposed design scheme can be guaranteed and the multi-variate case is also discussed. In order to validate the design approach, the simulation results are provided to show the effectiveness of the proposed algorithm.

Stochastic systems can be widely adopted for describing practical complex systems, such as meteorology. Recently, there have been many advances in the design of stochastic systems, including system modeling, control, estimation, performance enhancement, and industrial applications. Motivated by these results, this Special Issue encourages researchers to publish their latest contributions in the study of stochastic systems. In summary, we first introduce the current technical challenges in stochastic systems. Then, a current prevalent problem is provided to demonstrate the challenges in these systems, while the developing trends for stochastic system research are summarised. In particular, data-driven non-Gaussian system analyses will be the one of the significant research focal points in future.

No abstract