Neuro-Optimal Trajectory Tracking With Value Iteration of Discrete-Time Nonlinear Dynamics

Area of Science:

• Control Theory
• Nonlinear Systems
• Artificial Intelligence

Background:

• Discrete-time nonlinear systems present challenges for precise trajectory tracking.
• Existing control methods may struggle with optimality and stability guarantees.

Purpose of the Study:

• To develop a novel neuro-optimal tracking control approach for discrete-time nonlinear systems.
• To transform trajectory tracking into an optimal regulation problem for enhanced control design.

Main Methods:

• Constructing a new augmented plant to reformulate the control problem.
• Employing a value-iteration-based tracking control algorithm with convergence analysis.
• Estimating approximation errors between iterative and optimal value functions.
• Implementing an iterative heuristic dynamic programming (HDP) algorithm with novel updating rules.

Main Results:

• The steady control input for reference trajectory tracking is determined.
• Convergence of the value function sequence is mathematically established.
• Uniformly ultimately bounded stability of the closed-loop system is demonstrated.
• The proposed controller shows optimality and effectiveness in simulation examples.

Conclusions:

• The developed neuro-optimal control approach effectively addresses trajectory tracking in discrete-time nonlinear systems.
• The heuristic dynamic programming implementation provides a robust method for controller design.
• The method ensures system stability and controller optimality, validated by examples.