Distributed learning algorithm for non-linear differential graphical games

Abstract

This paper introduces differential graphical games for continuous-time non-linear systems and proposes an online adaptive learning framework. The error dynamics and the user-defined performance indices of each agent depend only on local information and the proposed cooperative learning algorithm learns the solution to the cooperative coupled Hamilton–Jacobi equations. In the proposed algorithm, each one of the agents uses an actor/critic neural network (NN) structure with appropriate tuning laws in order to guarantee closed-loop stability and convergence of the policies to the Nash equilibrium. Finally, a simulation example verifies the effectiveness of the proposed approach.

Observer‐based adaptive optimal output containment control problem of linear heterogeneous Multiagent systems with relative output measurements

“…where Ψ i satisfies the discounted ARE (48). Substituting (46), (47), and (44) into (45) yields the discounted ARE as follows:…”

“…Another important issue, which is not considered in the existing results for containment control, is designing online solutions that do not require having access to the complete knowledge of the leaders by all followers (fourth limitation). Reinforcement learning (RL) 33,34 has been successfully used to design adaptive optimal controllers for single-agent systems [35][36][37][38][39][40][41][42][43] and multiagent systems [44][45][46][47][48] online. However, to our knowledge, there is no RL-based solution to the optimal output containment control problem.…”

Intelligent Distributed Cooperative Control for Multiple Nonholonomic Mobile Robots Subject to Unknown Dynamics and External Disturbances

“…n p v a n q q I g q v η I g q e (15) Next, the pseudo-control inputs of (10) and the real-control inputs of (11) are defined as…”

“…They could not be directly applied to nonlinear systems. In [15], the global optimal synchronization scheme was proposed, although it ignored external disturbances. In [16], a distributed control scheme was proposed to reject the external disturbances; however, the optimal criterion was not applied therein.…”

“…The use of a large number of NNs was an essential requirement for traditional ADP-based cooperative optimal control schemes [11,12,15,20], especially the schemes concerning external disturbances. Most recently, in [14], for multiple linear agents, Jiao, et al presented a scheme that used the so-called actor-critic-disturber (ACD) structure, consisting of a critic NN, an actor NN and a disturber NN, to approximate optimal value functions, optimal control laws, and disturbance laws, respectively.…”