Adaptive dynamic programming for containment control with robustness analysis to iterative error: A global Nash equilibrium solution.
ISA Trans
; : 1-15, 2024 Aug 28.
Article
in En
| MEDLINE
| ID: mdl-39261266
ABSTRACT
Global Nash equilibrium is an optimal solution for each player in a graphical game. This paper proposes an iterative adaptive dynamic programming-based algorithm to solve the global Nash equilibrium solution for optimal containment control problem with robustness analysis to the iterative error. The containment control problem is transferred into the graphical game formulation. Sufficient conditions are given to decouple the Hamilton-Jacobi equations, which guarantee the solvability of the global Nash equilibrium solution. The iterative algorithm is designed to obtain the solution without any knowledge of system dynamics. Conditions of iterative error for global stability are given with rigorous proof. Compared with existing works, the design procedures of control gain and coupling strength are separated, which avoids trivial cases in the design procedure. The robustness analysis exactly quantifies the effect of the iterative error caused by various sources in engineering practice. The theoretical results are validated by two numerical examples with marginally stable and unstable dynamics of the leader.
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Language:
En
Journal:
ISA Trans
Year:
2024
Document type:
Article
Country of publication:
United States