Multi-agent graphical games with input constraints:an online learning solution

This paper studies an online iterative algorithm for solving discrete-time multi-agent dynamic graphical games with input constraints.In order to obtain the optimal strategy of each agent,it is necessary to solve a set of coupled Hamilton-Jacobi-Bellman(HJB)equations.It is very difficult to solve HJB equations by the traditional method.The relevant game problem will become more complex if the control input of each agent in the dynamic graphical game is constrained.In this paper,an online iterative algorithm is proposed to find the online solution to dynamic graphical game without the need for drift dynamics of agents.Actually,this algorithm is to find the optimal solution of Bellman equations online.This solution employs a distributed policy iteration process,using only the local information available to each agent.It can be proved that under certain conditions,when each agent updates its own strategy simultaneously,the whole multi-agent system will reach Nash equilibrium.In the process of algorithm implementation,for each agent,two layers of neural networks are used to fit the value function and control strategy,respectively.Finally,a simulation example is given to show the effectiveness of our method.

Fabrication of Pyrene and Tetraphenylethylene Nanostructures by a Hydrolysis-Assisted Co-Assembly

The poly(allylamine hydrochloride)-g-pyrene-tetraphenylethylene(PAH-g-Py-g-TPE)copolymers with different ratios of Py and TPE are synthesized by grafting 1-pyrenecarboxaldehyde(Py-CHO)and tetraphenylethylene-carboxaldehyde(TPE-CHO)to PAH via a Schiff base reaction in methanol.The PAH-g-Py-g-TPE forms spherical micelles in water regardless of the ratios of Py and TPE,which can transform into different nanostructures after being incubated in pH 0 and pH 2 solutions,respectively.These nanomaterials including nanoparticles(NPs),nano-rods(NRs),nanotubes(NTs)and nanoribbons(NBs)are composed of Py-CHO and TPE-CHO with different ratios,and emit fluorescence with colors different from the pure Py NRs and NTs,and TPE NPs.