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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
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Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method.

Yi Yang1, Yong Zhang1, Yuyang Zhou2

  • 1School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China.

Entropy (Basel, Switzerland)
|February 25, 2023
PubMed
Summary

This study introduces a new stochastic control framework for output probability density function (PDF) tracking. The novel method effectively manages multiplicative noises and time-varying references, outperforming traditional approaches like the linear-quadratic regulator (LQR).

Keywords:
B-spline modelfull probability designprobability density functiontracking control

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Area of Science:

  • Control Theory
  • Stochastic Systems
  • Probability Density Functions

Background:

  • Output probability density function (PDF) tracking in stochastic systems presents significant theoretical and practical challenges.
  • Existing methods often struggle with complex dynamics, model errors, and time-varying targets.

Purpose of the Study:

  • To develop a novel stochastic control framework for precise output PDF tracking of time-varying references.
  • To address the challenges posed by multiplicative noises and model uncertainties in stochastic systems.

Main Methods:

  • Characterizing output PDF using B-spline model approximation for weight dynamics.
  • Modeling system uncertainties with multiplicative noises to establish stochastic dynamics.
  • Developing an extended fully probabilistic design (FPD) to handle noise and time-varying references.

Main Results:

  • The PDF tracking problem is successfully transformed into a state tracking problem for weight dynamics.
  • The extended FPD framework demonstrates superior performance in managing multiplicative noises and time-varying targets.
  • Numerical examples and comparative simulations validate the proposed framework's effectiveness.

Conclusions:

  • The proposed stochastic control framework offers a robust solution for output PDF tracking of time-varying references.
  • The extended FPD approach provides enhanced control capabilities for stochastic systems with multiplicative noises.
  • This work advances the field of stochastic control, offering a superior alternative to methods like LQR.