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Zero-sum game-based dynamic self-triggered sliding mode control for unknown nonlinear systems with asymmetric input

Ning Xu¹, Tengda Wang², Ben Niu³

¹College of Information Science and Technology, Bohai University, Jinzhou 121013, Liaoning, China.

ISA Transactions

|November 20, 2025

Summary

This study introduces a novel adaptive dynamic programming approach for controlling unknown nonlinear systems with input constraints. The method ensures system stability and optimal performance using a dynamic self-triggered sliding mode control strategy.

Keywords:

Adaptive dynamic programming Data-driven method Dynamic self-triggered mechanism Input constraint Zero-sum game

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Area of Science:

Control Theory
Nonlinear Systems
Adaptive Dynamic Programming

Background:

Controlling unknown nonlinear systems with asymmetric input constraints presents significant challenges.
Existing methods often struggle with real-time adaptation and computational efficiency.

Purpose of the Study:

To develop a robust control strategy for unknown continuous-time nonlinear systems with asymmetric input constraints.
To address the zero-sum game-based dynamic self-triggered sliding mode control problem.

Main Methods:

Formulation of a novel nonquadratic value function to convert H-infinity control into an unconstrained zero-sum game.
Utilizing recurrent neural networks for data-driven reconstruction of unknown system dynamics.
Design of a dynamic self-triggered mechanism for adaptive determination of triggering instants.

Main Results:

A streamlined single-critic neural architecture is proposed to solve the Hamilton-Jacobi-Isaacs equation, eliminating actor-network dependency.
Lyapunov-based analysis guarantees uniform ultimate boundedness of all closed-loop signals.
The control strategy demonstrated excellent dynamic response characteristics in simulations.

Conclusions:

The proposed adaptive dynamic programming method effectively addresses the control of unknown nonlinear systems with asymmetric input constraints.
The dynamic self-triggered sliding mode control strategy ensures system stability and optimal performance.
Validated on robotic arm and microgrid systems, showcasing practical applicability and robustness.