Performance Assessment of Non-Gaussian Control Systems Based on Chi-square

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Performance Assessment of Non-Gaussian Control Systems Based on Chi-square

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[1]ZHANG Jinfang,QIAO Beibei.Performance Assessment of Non-Gaussian Control Systems Based on Chi-square[J].Journal of Zhengzhou University (Engineering Science),2027,48(XX):1-10.[doi:10.13705/j.issn.1671-6833.2026.06.012]

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Journal of Zhengzhou University (Engineering Science)[ISSN 1671-6833/CN 41-1339/T] Volume: 48 Number of periods: 2027 XX Page number: 1-10 Column: Public date: 2027-12-10

Title:: Performance Assessment of Non-Gaussian Control Systems Based on Chi-square

Author(s):: ZHANG Jinfang¹, QIAO Beibei^1,2; 1.School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China; 2.State Grid Jibei Electric Power Company Limited Smart Distribution Network Center, Qinhuangdao 066100, China

Keywords:: non-gaussian systems; chi-square index; performance assessment; parameter identification

CLC:: TP14

DOI:: 10.13705/j.issn.1671-6833.2026.06.012

Abstract:: A study was conducted to address the shift-invariance defect of entropy-based indices and the unboundedness problem of the chi-square statistic in evaluating the performance of non-Gaussian control systems. A Chi-square-based performance index was proposed, and the particle swarm optimization algorithm was enhanced with an elite-population strategy to enable faster and more accurate estimation of the benchmark output by identifying unknown system parameters and the probability density functions of disturbance noise; the benchmark output was subsequently computed using feedback invariants. The proposed index assessed system performance by calculating the Chi-square distance between the benchmark and actual output distributions, effectively mitigating the drawbacks of entropy indices, including large data requirements, long computation time, and sensitivity to mean shifts. Simulation studies conducted on univariate and multivariate systems under different noise conditions showed that the identified parameters were closer to the true values and that the required number of iterations decreased by an average of 73.4%. In multivariate scenarios where covariance matrices shared the same trace, the minimum-variance index was unable to differentiate among distributional states, whereas the Chi-square index provided significant discrimination (from 0.89 to 0.45), demonstrating its higher evaluation accuracy, greater sensitivity, and broader applicability

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Last Update: 2026-06-29