Performance Assessment of Non-Gaussian Control Systems Based on Mixture Correntropy

Abstract

The performance assessment of any control system plays a key role in industrial control systems. To meet the real-time requirements of modern control systems, a quick and accurate evaluation of the performance of a system is necessary. In this paper, a performance assessment method of a non-Gaussian control system based on mixture correntropy is proposed for non-Gaussian stochastic systems. Mixture correntropy can solve the problem of minimum entropy translation invariance. When the expected output of a system is unavailable, mixture correntropy combined with the estimation of distribution algorithm (EDA) is used for system identification and noise distribution estimation so as to calculate the benchmark of entropy-based performance assessment. When the expected output of a system is available, the mixture correntropy is directly used as the index to evaluate the performance of the system. To improve the real-time aspect of the performance assessment, an improved EDA is presented to obtain the evaluation index more quickly. For both Gaussian and non-Gaussian systems, the mixture correntropy and the improved identification algorithm are used for system performance assessment, and the results are compared with the minimum entropy index and the probability density function (PDF) curve coincident area index. The comparisons verify the rationality and effectiveness of the correntropy index and the rapidity of the improved EDA algorithm.

Generalized Correntropy Criterion-Based Performance Assessment for Non-Gaussian Stochastic Systems

“…The mixture correntropy index is adopted by Zhang [ 13 ] to solve the problem of translation invariance. However, the Gaussian kernel is applied to the kernel function of mixture correntropy in [ 13 ], which is not comprehensive in describing the statistical properties of non-Gaussian random variables [ 16 ]. As mentioned before, generalized correntropy is a more appropriate indicator.…”

“…For the above example, the parameter vector to be identified is . Most of the initial parameters are based on the previous works [ 12 , 13 , 14 , 31 , 32 , 33 ]. Generally, in the EDA, the number of individuals in the initial population is ; the optimal number of individuals for each iteration is ; and the maximum number of iterations is .…”

“…Therefore, the application effect of MEC control strategy is much better than MVC in non-Gaussian systems. On this basis, some significant progress has been made in the field of CPA with non-Gaussian noise [ 9 , 10 , 11 , 12 , 13 , 14 ]. When the expected output PDF is not given in advance, it is necessary for the CPA methods of the controlled system based on MEC to identify the associated system model effectively and systematically based on closed-loop data.…”

“…When the mean of error distribution is not around zero, the wrong assessment result may be caused. For this case, Zhou proposed the performance index of mean-constraint, while a CPA method based on mixture correntropy was proposed by Zhang [ 13 ]. The problem of the minimum entropy translation invariance can be solved by adjust the kernel width and weight coefficient of mixture correntropy.…”

“…Correntropy is a measure of the generalized similarity of two random variables using information from the statistical properties of higher-order signals [ 15 ]. The kernel function of mixture correntropy CPA [ 13 ] is Gaussian kernel by default. However, it can only reflect a specific type of noise with Gaussian function, and the shape of entropy cannot be changed freely.…”