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Non-Gaussian disturbance rejection control for multivariate stochastic systems using moment-generating function.

Jianhua Zhang1, Jinzhu Pu2, Mifeng Ren3

  • 1State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206, China.

ISA Transactions
|May 25, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new control algorithm to reduce non-Gaussian disturbances in nonlinear stochastic systems. The method uses minimum entropy principles to improve system stability and performance, demonstrating effectiveness through simulations.

Keywords:
Disturbance rejection controlMoment-generating functionsNon-Gaussian stochastic systems

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Area of Science:

  • Control Theory
  • Stochastic Systems
  • Nonlinear Dynamics

Background:

  • Nonlinear multivariate stochastic systems present challenges in disturbance rejection.
  • Existing control methods may not adequately address non-Gaussian disturbances.
  • Minimum entropy principles offer a promising approach for robust control design.

Purpose of the Study:

  • To develop a non-Gaussian disturbance rejection control algorithm for nonlinear multivariate stochastic systems.
  • To propose a novel performance criterion based on minimum entropy for stochastic systems.
  • To analyze the stability and effectiveness of the proposed control strategy.

Main Methods:

  • Derivation of moment-generating functions from probability density functions of output tracking errors.
  • Development of a time-variant linear model using sampled moment-generating functions.
  • Design of a control algorithm minimizing a newly proposed entropy-based criterion.
  • Stability analysis of the closed-loop control system.

Main Results:

  • A novel non-Gaussian disturbance rejection control scheme is proposed.
  • The randomness of the stochastic nonlinear system is effectively attenuated.
  • Theoretical convergence analysis confirms the stability of the control system.
  • Simulation results validate the algorithm's effectiveness.

Conclusions:

  • The developed control algorithm successfully rejects non-Gaussian disturbances in nonlinear stochastic systems.
  • The minimum entropy-based criterion provides a robust approach to enhance system performance.
  • The study establishes a framework for controlling general stochastic systems.