Probability density function (PDF) control strategy investigates the controller design approaches where the random variables for the stochastic processes were adjusted to follow the desirable distributions. In other words, the shape of the system PDF can be regulated by controller design.Different from the existing stochastic optimization and control methods, the most important problem of PDF control is to establish the evolution of the PDF expressions of the system variables. Once the relationship between the control input and the output PDF is formulated, the control objective can be described as obtaining the control input signals which would adjust the system output PDFs to follow the pre-specified target PDFs. Motivated by the development of data-driven control and the state of the art PDF-based applications, this paper summarizes the recent research results of the PDF control while the controller design approaches can be categorized into three groups: (1) system model-based direct evolution PDF control; (2) model-based distribution-transformation PDF control methods and (3) data-based PDF control. In addition, minimum entropy control, PDF-based filter design, fault diagnosis and probabilistic decoupling design are also introduced briefly as extended applications in theory sense.

This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems, which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using a radial basis function neural network, while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated, while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design, which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given, which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be summarized as follows: 1) an output entropy model is presented using a neural network; 2) a nonlinear filter design algorithm is developed as the main result; and 3) a solution of the entropy assignment problem is obtained, which is an extension of the presented framework.

In this paper, a novel control algorithm is presented to enhance the performance of the tracking property for a class of nonlinear and dynamic stochastic systems subjected to non-Gaussian noises. Although the existing standard PI controller can be used to obtain the basic tracking of the systems, the desired tracking performance of the stochastic systems is difficult to achieve due to the random noises. To improve the tracking performance, an enhanced performance loop is constructed using the EKF-based state estimates without changing the existing closed loop with a PI controller. Meanwhile, the gain of the enhanced performance loop can be obtained based upon the entropy optimization of the tracking error. In addition, the stability of the closed loop system is analyzed in the mean-square sense. The simulation results are given to illustrate the effectiveness of the proposed control algorithm.

In this technical note, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.

Concrete is the main material in building. Since its poor structural integrity may cause accidents, it is significant to detect defects in concrete. However, it is a challenging topic as the unevenness of concrete would lead to the complex dynamics with uncertainties in the ultrasonic diagnosis of defects. Note that the detection results mainly depend on the direct parameters, e.g., the time of travel through the concrete. The current diagnosis accuracy and intelligence level are difficult to meet the design requirement for automatic and increasingly high-performance demands. To solve the mentioned problems, our contribution of this paper can be summarized as establishing a diagnosis model based on the GA-BPNN method and ultrasonic information extracted that helps engineers identify concrete defects. Potentially, the application of this model helps to improve the working efficiency, diagnostic accuracy and automation level of ultrasonic testing instruments. In particular, we propose a simple and effective signal recognition method for small-size concrete hole defects. This method can be divided into two parts: (1) signal effective information extraction based on wavelet packet transform (WPT), where mean value, standard deviation, kurtosis coefficient, skewness coefficient and energy ratio are utilized as features to characterize the detection signals based on the analysis of the main frequency node of the signals, and (2) defect signal recognition based on GA optimized back propagation neural network (GA-BPNN), where the cross-validation method has been used for the stochastic division of the signal dataset and it leads to the BPNN recognition model with small bias. Finally, we implement this method on 150 detection signal data which are obtained by the ultrasonic testing system with 50 kHz working frequency. The experimental test block is a C30 class concrete block with 5, 7, and 9 mm penetrating holes. The information of the experimental environment, algorithmic parameters setting and signal processing procedure are described in detail. The average recognition accuracy is 91.33% for the identification of small size concrete defects according to experimental results, which verifies the feasibility and efficiency.

This note presents a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing st