Approximate-optimal control algorithm for constrained zero-sum differential games through event-triggering mechanism

This paper investigates the optimization problem of two-player zero-sum differential game with control constraints in the framework of event triggering. Relying on reinforcement learning, an adaptive dynamic programming algorithm is developed to approximate the optimal solution of zero-sum game, i.e...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics Vol. 95; no. 4; pp. 2639 - 2657
Main Authors: Mu, Chaoxu, Wang, Ke
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.03.2019
Springer Nature B.V
Subjects:
Adaptive algorithms
Automotive Engineering
Classical Mechanics
Closed loops
Communication
Constraints
Control
Control algorithms
Control theory
Design
Differential games
Distance learning
Dynamic programming
Dynamical Systems
Engineering
Equilibrium
Feedback control
Game theory
Machine learning
Mathematical analysis
Mechanical Engineering
Neural networks
Optimal control
Optimization
Original Paper
Saddle points (game theory)
Teaching methods
Vibration
Zero sum games
Neural network (NN)
Event triggering
Zero-sum differential game
Control constraints
Adaptive dynamic programming (ADP)
ISSN:0924-090X, 1573-269X
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper investigates the optimization problem of two-player zero-sum differential game with control constraints in the framework of event triggering. Relying on reinforcement learning, an adaptive dynamic programming algorithm is developed to approximate the optimal solution of zero-sum game, i.e., the saddle-point equilibrium. A single-network structure is adopted, wherein a critic neural network (NN) evaluates the action. First, the constrained Hamilton–Jacobi–Isaacs equation is mathematically derived in the presence of control constraints; the event-triggering mechanism is then incorporated to reduce calculations and actions. Then, based on the gradient-descent technique, a novel weight updating law is designed for the critic NN, which ensures the solution can converge to the optimal value online. Moreover, the stability of closed-loop system is guaranteed and the unfavorable Zeno behavior is excluded by calculating the theoretical minimum triggering interval. Finally, two numerical examples are provided to verify the reliability and effectiveness of proposed algorithm.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4713-0