Prescribed-time distributed Nash equilibrium seeking for noncooperation games

Prescribed-Time Nash Equilibrium Seeking for Pursuit-Evasion Game

“…In response to the issue of convergence rate heavily relying on the players' initial conditions, the fixed-time [16]- [18] Nash equilibrium seeking algorithms were employed for noncooperative games [19]. The first-order fixed-time algorithm was designed to achieve exact convergence to the Nash equilibrium of the game in [19]. However, the fixed-time bounds can be defined by the system designer under an appropriate tuning of the parameters of the algorithms.…”

“…Building on these excellent cornerstone results, the control algorithm designed in this letter is motivated by two main objectives. Firstly, notice that the existing Nash equilibrium seeking algorithms are established over asymptotic convergence [6] or fixed-time convergence [19]. For PEG, the evaders should be captured within a prescribed-time which means the convergence time can be pre-designed.…”

Fixed-Time Consensus-Based Nash Equilibrium Seeking

“…However, the convergence time of the finite-time result is related to the initial conditions, which are not always available in practice. To overcome this disadvantage, the authors of [20] proposed a fixed-time NE seeking algorithm based on extreme seeking. The prescribed-time algorithms were developed based on the motion-planning method in [21] and the time base gen-erator in [22].…”

“…A new Lyapunov function is designed to prove fixed-time convergence. Moreover, it is a distinct method from that presented in [20]. The explicit form of the settling time is given, which is independent of the initial conditions and only relies on the design parameters, allowing it to be predetermined prior to system operation.…”

Prescribed-Time Fully Distributed Nash Equilibrium Seeking Strategy in Networked Games

“…To meet this requirement, various distributed control strategies have been presented. For example, a distributed timevarying seeking strategy that utilizes a prescribed-time observer under undirected graphs was proposed to achieve the convergence within a set time [12]. Utilizing the distributed motion-planning method and the gradient search, a class of prescribed-time distributed Nash equilibrium seeking algorithms have been developed for first and second order multi-agent systems [13].…”