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Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input.

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Neural Networks : the Official Journal of the International Neural Network Society
|June 25, 2017
PubMed
Summary

This study introduces an identifier-critic structure using neural networks to create an online controller for nonlinear systems with control saturation. The method ensures system stability and accurate approximation of unknown dynamics without prior system knowledge.

Keywords:
Adaptive controlNeural networksNonaffine nonlinear systemsOptimal control

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Artificial Intelligence

Background:

  • Controlling continuous-time nonaffine nonlinear systems with saturated control signals presents significant challenges.
  • Traditional methods often require precise knowledge of system dynamics, which is frequently unavailable in real-world applications.
  • The Hamilton-Jacobi-Bellman (HJB) equation is central to optimal control but difficult to solve for complex systems.

Purpose of the Study:

  • To develop an online, near-optimal control strategy for continuous-time nonaffine nonlinear systems with control saturation.
  • To address the challenge of unknown system dynamics by employing adaptive neural network techniques.
  • To ensure the control signal remains within specified saturation bounds while maintaining system stability.

Main Methods:

  • An identifier-critic structure utilizing two Neural Networks (NNs) is proposed.
  • The identifier NN approximates unknown system dynamics, while the critic NN approximates the value function by solving the HJB equation.
  • Online simultaneous tuning of NN weights ensures accurate approximation and adherence to control saturation limits, validated by Lyapunov's direct method.

Main Results:

  • The proposed method successfully derives a near-optimal controller without prior knowledge of system dynamics.
  • Simultaneous online tuning of identifier and critic NNs guarantees accurate approximation of unknown terms and keeps the control signal within saturation bounds.
  • Convergence of NN weights, identification error, and system states is mathematically proven using Lyapunov's direct method.

Conclusions:

  • The identifier-critic structure with neural networks provides an effective solution for controlling nonlinear systems with control saturation.
  • The adaptive nature of the NNs allows for online learning and control, making the strategy robust to uncertainties.
  • Simulation results on two nonlinear systems validate the effectiveness and practical applicability of the proposed control strategy.