Proposal “ New Results in Systems and Control ”

Consider a controlled evolutionary game (CEG), where nn players, xxii , ii = 1,⋯ ,nn, are considered as machines and mm players, uuii , ii = 1, ... ,mm, are considered as human players. Assume the machines strategy updating rules are known, and their payoffs yyii, ii = 1, ... ,nn, are also known. Then the dynamic model can be described as � xx1(tt + 1) = ff1(xx1,⋯ , xxnn,uu1,⋯ , uumm) ⋮ xxnn(tt + 1) = ffnn(xx1,⋯ , xxnn,uu1,⋯ ,uumm) yyjj(tt) = ccjj(xx1,⋯ , xxnn,uu1,⋯ ,uumm), jj = 1,⋯ ,nn, where xxpp ∈ DDkk,pp = 1, ... ,nn and uuqq ∈ DDkk, qq = 1, ... ,mm are kk -valued logical variables, ffii: DDkk → DDkk, ii = 1, ... ,nn are logical functions, and ccjj: DDkk → R, jj = 1, ... ,nn are pseudological functions. First, we give a necessary and sufficient condition to judge whether a CEG is observable. That is, for any two initial states xx0 ≠ ?̅?x can we find a control sequence uu0, uu1, ... ,uuss, ss < ∞, such that the outputs yy(xx0,uu0,⋯ ,uuss) ≠ yy(?̅?x0,uu0,⋯ ,uuss)? Secondly, we prove that if a CEG is observable, then we can find a control sequence uu0,uu1, ... ,uuss, ss < ∞, such that the initial state xx0 is identifiable. An algorithm is provided to calculate it. The importance of this work is: Though the strategies xxii(tt) may completely unknown, it can be recognized via observed payoffs. And then the optimal control and all other control goals can be realized. Paper 6: Title: Distributed output tracking of multi-agent systems with stochastic nonlinear dynamics and multiple leaders Authors: Wuquan Li, Lu Liu and Gang Feng, City University of Hong Kong, Hong Kong, China. Abstract: The distributed output tracking problem is studied for multi-agent systems with stochastic nonlinear dynamics and multiple leaders. For the case where the graph topology is directed and the leaders set is the neighbor of only a small portion of followers, distributed tracking controllers are designed to ensure that the followers’ outputs will exponentially converge to the convex hull spanned by the dynamic leaders’ outputs with tunable tracking errors while all the states of the closed-loop system remain bounded in probability. The efficiency of the tracking controllers is demonstrated by a simulation example.