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Adaptive tracking control for stochastic nonlinear systems with time-varying delays using multi-dimensional Taylor

Hong-Sen Yan1, Guo-Biao Wang1

  • 1School of Automation, Southeast University, Nanjing, Jiangsu, China; Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Nanjing, Jiangsu, China.

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|June 25, 2022
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Summary

This study introduces an adaptive control scheme for stochastic nonlinear systems (SNSs) facing uncertainties and delays. The novel method enhances tracking performance and system robustness, outperforming traditional approaches.

Keywords:
Deep deterministic policy gradientFast time-varying perturbationMulti-dimensional Taylor networkStochastic nonlinear systemTime-varying delay

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Machine Learning Applications

Background:

  • Conventional model-based control for stochastic nonlinear systems (SNSs) struggles with uncertainties, leading to conservatism, slow convergence, and poor anti-interference. Existing methods often require known evolution behaviors of uncertain variables, limiting practical application.
  • Fast time-varying uncertainties, stochastic disturbances, and unknown time-varying delays pose significant challenges to the control of SNSs, demanding advanced adaptive control strategies.

Purpose of the Study:

  • To develop an adaptive control scheme for addressing the tracking problem in stochastic nonlinear systems (SNSs) with complex uncertainties, stochastic disturbances, and unknown time-varying delays.
  • To improve the real-time performance, convergence speed, and anti-interference capabilities compared to conventional model-based control methods.

Main Methods:

  • An adaptive control scheme integrating Deep Deterministic Policy Gradient (DDPG) and Multi-Dimensional Taylor Network (MTN) is proposed.
  • Time delays are managed by embedding them in a reproducing kernel Hilbert space via error coordinate transformation.
  • A novel persistent excitation (PE) mechanism is introduced to enhance robustness against fast time-varying uncertainties, ensuring policy adaptation and convergence.

Main Results:

  • The Multi-Dimensional Taylor Network (MTN) acts as a surrogate within the DDPG framework, constructing online and target networks using the temporal-difference method for improved real-time performance.
  • The persistent excitation (PE) mechanism ensures exponential convergence of MTN weights, driving the system towards the target trajectory.
  • Theoretical analysis using Lyapunov-Krasovskii functional proves that tracking errors and closed-loop states are uniformly ultimately bounded (UUB).

Conclusions:

  • The proposed DDPG and MTN-based adaptive control scheme effectively addresses the tracking problem for stochastic nonlinear systems (SNSs) under challenging conditions.
  • The method demonstrates superior real-time performance, robustness, and convergence compared to traditional approaches.
  • Numerical simulations in the process industry validate the practical effectiveness and reliability of the developed control strategy.