<p>This paper presents a novel error-driven flexible prescribed performance <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> controller (ED-FPPC-<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>) for nonlinear systems, addressing the dual challenges of asymmetric state constraints and actuator saturation. An asymmetric state transformation technique is employed to confine tracking errors within predefined boundaries, while an innovative error-driven flexible prescribed performance control (FPPC) mechanism dynamically adjusts these boundaries based on real-time system state proximity to constraints. The proposed approach integrates robust <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> control for disturbance attenuation with a Hamilton-Jacobi-Isaacs (HJI) equation formulation that balances control optimality against worst-case disturbance scenarios. A single-critic neural network (SCNN) facilitates online learning of the optimal control policy via reinforcement learning. The error-driven FPPC mechanism prevents constraint violations during severe disturbances while maintaining prescribed performance guarantees during normal operation. Lyapunov stability analysis validates the uniform ultimate boundedness of all closed-loop signals. Simulations demonstrate that the controller maintains prescribed tracking accuracy with adaptive boundary relaxation capability amidst actuator saturation and external disturbances.</p>

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Error-driven flexible prescribed performance \(H_{\infty }\) adaptive critic control with asymmetric state constraints and actuator saturation

  • Shuangsi Xue,
  • Junkai Tan,
  • Xiaotian Liang,
  • Hui Cao,
  • Badong Chen

摘要

This paper presents a novel error-driven flexible prescribed performance \(H_{\infty }\) H controller (ED-FPPC- \(H_{\infty }\) H ) for nonlinear systems, addressing the dual challenges of asymmetric state constraints and actuator saturation. An asymmetric state transformation technique is employed to confine tracking errors within predefined boundaries, while an innovative error-driven flexible prescribed performance control (FPPC) mechanism dynamically adjusts these boundaries based on real-time system state proximity to constraints. The proposed approach integrates robust \(H_{\infty }\) H control for disturbance attenuation with a Hamilton-Jacobi-Isaacs (HJI) equation formulation that balances control optimality against worst-case disturbance scenarios. A single-critic neural network (SCNN) facilitates online learning of the optimal control policy via reinforcement learning. The error-driven FPPC mechanism prevents constraint violations during severe disturbances while maintaining prescribed performance guarantees during normal operation. Lyapunov stability analysis validates the uniform ultimate boundedness of all closed-loop signals. Simulations demonstrate that the controller maintains prescribed tracking accuracy with adaptive boundary relaxation capability amidst actuator saturation and external disturbances.