Mapping Tracking Control to Cascading Optimization in Discrete Strict-Feedback Systems: A Hierarchical Learning...

Area of Science:

• Control Systems Engineering
• Machine Learning
• Optimization Theory

Background:

• Discrete-time (DT) systems with strict feedback structures pose challenges for traditional tracking control.
• Existing methods like backstepping may not fully address the complexities of adaptive control in such systems.

Purpose of the Study:

• To introduce a novel hierarchical learning (HL) framework for discrete-time systems with strict feedback.
• To enable effective tracking control by dynamically adjusting virtual targets (VTs) and facilitating inter-layer self-optimization.

Main Methods:

• A hierarchical learning framework with dynamically adjustable virtual targets (VTs) for state variables.
• Approximation of the discrete-time Hamilton-Jacobi-Bellman (HJB) equation at each layer for self-optimization.
• An iterative predictive learning framework to address noncausality and align VTs with optimal trajectories.
• Transformation of the action network into a tracking network incorporating future tracking errors.

Main Results:

• The proposed HL framework enables indirect tracking of state variables towards desired targets.
• The method optimizes tracking network weights by considering future tracking errors, reducing costs and improving performance.
• Convergence analysis and numerical simulations demonstrate the framework's effectiveness.

Conclusions:

• The hierarchical learning framework offers a powerful approach for adaptive tracking control in discrete-time systems.
• The dynamic VT adjustment and iterative learning contribute to enhanced control performance and system stability.
• This method shows significant potential for applications in adaptive control engineering.