Open AccessFinite‐horizon optimal tracking control for constrained‐input nonlinear interconnected system using aperiodic distributed nonzero‐sum games
Author(s) -
Duan Dandan,
Liu Chunsheng
Publication year - 2021
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12116
Subject(s) - aperiodic graph , control theory (sociology) , differential game , bounded function , mathematics , tracking error , optimal control , riccati equation , controller (irrigation) , observability , mathematical optimization , zero sum game , nonlinear system , lyapunov function , computer science , differential equation , nash equilibrium , control (management) , physics , combinatorics , quantum mechanics , artificial intelligence , mathematical analysis , agronomy , biology
This paper proposes a distributed adaptive dynamic programming scheme to investigate the optimal tracking control problem for finite‐horizon non‐linear interconnected systems with constraint inputs under aperiodic sampling. A N‐player nonzero‐sum differential game system is constructed with the presented non‐linear interconnected system and the tracking error system by introducing the augment vectors. To address the problems of constrained‐input and finite‐horizon control, a non‐quadratic utility function and a finite‐horizon cost function are utilized which will arise in the time‐varying Hamilton–Jacobi (HJ) equation. Then, a periodic event‐triggered scheme is designed to realize aperiodic sampling, where the consumption of communication resources is reduced and the Zeno behavior is avoided. Under the designed periodic event‐triggered scheme, the time‐varying HJ equation is almost impossible to get an analytical solution due to its hybrid properties and non‐linearity. Therefore, the critic neural networks are used to estimate the optimal solution of the HJ equation, and the weight update law is constructed to guarantee the uniformly ultimate bounded of approximated errors. Further, the hybrid nonzero‐sum differential game is confirmed to be uniformly ultimate bounded by using the Lyapunov theory. Finally, the obtained distributed PET control strategy is successfully applied to dispose the missile‐target intercepter problem.