@ARTICLE{ iet:/content/journals/10.1049/iet-cta.2018.5464, author = {Chaoxu Mu}, author = {Ke Wang}, keywords = {optimal value;initial stabilising control policies;analyse;nonlinear system;approximate optimal critic;initial stabilising control laws;disturbance policies;zero-sum differential game;continuous-time zero-sum games;saddle-point equilibrium;two-player zero-sum game problems;improved approximate optimal control technique;continuous-time two-player zero-sum games;critic structure;critic neural network;zero-sum game problem;single-network ADP;single-network adaptive dynamic programming;value function;complex linear system;adaptive learning scheme;}, ISSN = {1751-8644}, language = {English}, abstract = {This study establishes an approximate optimal critic learning algorithm based on single-network adaptive dynamic programming aiming at solutions to continuous-time two-player zero-sum games in the absence of initial stabilising control policies. Single-network means one critic neural network, which is utilised to derive the saddle-point equilibrium of a zero-sum differential game by approximately learning the value function. First, the authors elaborate mathematically two-player zero-sum game problems and analyse the similarity of the zero-sum game problem between linear and non-linear systems. Then, this adaptive learning scheme is implemented as a critic structure that derives control and disturbance policies by learning the optimal value, and a novel weight tuning law involving a stable operator is proposed to ensure convergence and stability. Moreover, the uniform ultimate bounded stability of the whole system is rigorously proved by Lyapunov theory. Finally, reasonable simulation results are provided to confirm the effectiveness of the improved approximate optimal control technique in solving equations for a complex linear system and a non-linear system.}, title = {Single-network ADP for near optimal control of continuous-time zero-sum games without using initial stabilising control laws}, journal = {IET Control Theory & Applications}, issue = {18}, volume = {12}, year = {2018}, month = {December}, pages = {2449-2458(9)}, publisher ={Institution of Engineering and Technology}, copyright = {© The Institution of Engineering and Technology}, url = {https://digital-library.theiet.org/;jsessionid=jliwg8xhld9d.x-iet-live-01content/journals/10.1049/iet-cta.2018.5464} }