Stochastic distribution tracking control for stochastic non-linear systems via probability density function vectorisation

Abstract

This paper presents a new control strategy for stochastic distribution shape tracking regarding non-Gaussian stochastic non-linear systems. The objective can be summarised as adjusting the probability density function (PDF) of the system output to any given desired distribution. In order to achieve this objective, the system output PDF has first been formulated analytically, which is time-variant. Then, the PDF vectorisation has been implemented to simplify the model description. Using the vector-based representation, the system identification and control design have been performed to achieve the PDF tracking. In practice, the PDF evolution is difficult to implement in real-time, thus a data-driven extension has also been discussed in this paper, where the vector-based model can be obtained using kernel density estimation (KDE) with the real-time data. Furthermore, the stability of the presented control design has been analysed, which is validated by a numerical example. As an extension, the multi-output stochastic systems have also been discussed for joint PDF tracking using the proposed algorithm, and the perspectives of advanced controller have been discussed. The main contribution of this paper is to propose: (1) a new sampling-based PDF transformation to reduce the modelling complexity, (2) a data-driven approach for online implementation without model pre-training, and (3) a feasible framework to integrate the existing control methods.

Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications

“…To reduce the computational complexity, Hong Wang and Qichun Zhang present a series of alternative descriptions. For example, [13] presents a vector-based converted distance metric to achieve data-driven PDF tracking control. Similarly, the data-driven PID controller was obtained based on the PDF vectorisation in [14].…”

“…For system identification, the complexity depends on the number of system model parameters. For instance, [13] combined the least-square method, kernel density estimation and gradient descent algorithm, where the complexity analysis should be given separately and summed together in the end for the entire system design. Similarly, the neural network based design would contain high-complexity as the iteration occurs in each layer.…”

Fault isolation and fault‐tolerant control for nonlinear stochastic distribution control systems with multiplicative faults

“…Receiving inspiration from the fiber distribution in paper‐making systems, professor Hong Wang developed the stochastic distribution control (SDC) systems theory, which had been applied to the flame distribution in actual boilers and the molecular weight distribution of polymerization reactions 17‐21 . The ultimate purpose of SDC systems is to enable the shape of system output probability density function (PDF) to track the target shape 20,22 .…”

An improved Deeplabv3+ semantic segmentation algorithm with multiple loss constraints

“…Through the analysis of the above semantic segmentation algorithms, it can be seen that the mainstream semantic segmentation algorithms improve the accuracy of segmentation algorithms by using the underlying feature information, extracting multi-scale context information and attention mechanism. [21][22][23] Therefore, how to find appropriate underlying feature information to help restore images in the process of up-sampling, obtain more semantic information of scale and build appropriate attention mechanism module to enhance the dependency between pixels has become a hot research issue.…”