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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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Data-driven optimal tracking control for nonlinear systems with performance constraints via adaptive dynamic

Lulu Zhang1, Huaguang Zhang2, Xiaohui Yue1

  • 1College of Information Science and Engineering, Northeastern University, China.

Neural Networks : the Official Journal of the International Neural Network Society
|July 18, 2025
PubMed
Summary
This summary is machine-generated.

This study presents a data-driven control method for unknown nonlinear systems, ensuring optimal tracking within constraints. The approach uses adaptive dynamic programming and neural networks to achieve precise trajectory following and error minimization.

Keywords:
Adaptive dynamic programmingData-driven policy iterationNeural networksPrescribed performance

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Artificial Intelligence

Background:

  • Optimal tracking is crucial for nonlinear systems but challenging due to unknown dynamics and constraints.
  • Existing methods often require system model knowledge or struggle with simultaneous input and performance limitations.

Purpose of the Study:

  • To develop a data-driven optimal tracking control scheme for unknown nonlinear systems.
  • To ensure system states follow a desired trajectory while respecting input and performance constraints.
  • To minimize control cost and guarantee finite-time convergence of tracking errors.

Main Methods:

  • A finite-time performance function was used for error convergence.
  • A nonquadratic cost function and modified Hamilton-Jacobi-Bellman equation addressed input constraints.
  • An adaptive dynamic programming algorithm with actor-critic neural networks (NNs) learned the optimal control policy.
  • Least-squares method tuned NN weights using collected data.

Main Results:

  • The proposed scheme effectively achieved optimal tracking for unknown nonlinear systems.
  • Finite-time convergence of tracking errors within predefined zones was demonstrated.
  • Input constraints were strictly satisfied throughout the tracking process.
  • Simulations on Chua's circuit validated the algorithm's performance.

Conclusions:

  • The data-driven constrained optimal tracking control scheme is effective for unknown nonlinear systems.
  • The integration of adaptive dynamic programming and NNs offers a powerful approach to control design.
  • The method successfully balances tracking performance, cost minimization, and constraint satisfaction.