{"id":39475,"date":"2025-05-23T18:52:31","date_gmt":"2025-05-23T10:52:31","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/39475.html"},"modified":"2025-05-23T18:52:31","modified_gmt":"2025-05-23T10:52:31","slug":"matlab%e5%a4%9a%e6%99%ba%e8%83%bd%e4%bd%93%e7%bd%91%e7%bb%9c%e4%b8%80%e8%87%b4%e6%80%a7%e7%a0%94%e7%a9%b6","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/39475.html","title":{"rendered":"matlab\u591a\u667a\u80fd\u4f53\u7f51\u7edc\u4e00\u81f4\u6027\u7814\u7a76"},"content":{"rendered":"

\u4e00\u4e2a\u57fa\u4e8e\u8fde\u7eed\u65f6\u95f4\u591a\u667a\u80fd\u4f53\u7cfb\u7edf（Multi-Agent Systems, MAS）\u7684\u4e00\u9636\u4e00\u81f4\u6027\u534f\u8bae\u7684MATLAB\u4eff\u771f\u4ee3\u7801，\u5305\u542b\u7f51\u7edc\u62d3\u6251\u5efa\u6a21\u3001\u4e00\u81f4\u6027\u534f\u8bae\u8bbe\u8ba1\u548c\u6536\u655b\u6027\u5206\u6790\u3002\u4ee3\u7801\u652f\u6301\u56fa\u5b9a\u62d3\u6251\u548c\u65f6\u53d8\u62d3\u6251，\u9002\u7528\u4e8e\u5b66\u672f\u7814\u7a76\u3002<\/p>\n

\n

1. \u57fa\u7840\u6a21\u578b\u4e0e\u4ee3\u7801\u6846\u67b6<\/h4>\n

(1) \u7f51\u7edc\u62d3\u6251\u5efa\u6a21（\u56fe\u8bba）<\/h5>\n

\u5047\u8bbe\u6709 (N) \u4e2a\u667a\u80fd\u4f53，\u901a\u8fc7\u65e0\u5411\u56fe (G = (V, E)) \u8fde\u63a5，\u90bb\u63a5\u77e9\u9635\u4e3a (A)，\u5ea6\u77e9\u9635\u4e3a (D)，\u62c9\u666e\u62c9\u65af\u77e9\u9635 (L = D – A)\u3002<\/p>\n

% \u751f\u6210\u4e00\u4e2a\u5305\u542b5\u4e2a\u8282\u70b9\u7684\u73af\u5f62\u62d3\u6251<\/span>
\nN =<\/span> 5<\/span>;<\/span>
\nA =<\/span> zeros<\/span>(<\/span>N,<\/span> N)<\/span>;<\/span>
\nfor<\/span> i<\/span> =<\/span> 1<\/span>:<\/span>N
\n A<\/span>(<\/span>i<\/span>,<\/span> mod<\/span>(<\/span>i<\/span>,<\/span> N)<\/span>+<\/span>1<\/span>)<\/span> =<\/span> 1<\/span>;<\/span>
\n A<\/span>(<\/span>mod<\/span>(<\/span>i<\/span>,<\/span> N)<\/span>+<\/span>1<\/span>,<\/span> i<\/span>)<\/span> =<\/span> 1<\/span>;<\/span>
\nend<\/span>
\nL =<\/span> diag<\/span>(<\/span>sum<\/span>(<\/span>A,<\/span> 2<\/span>)<\/span>)<\/span> –<\/span> A;<\/span> % \u62c9\u666e\u62c9\u65af\u77e9\u9635<\/span><\/p>\n

\u53c2\u8003\u4ee3\u7801<\/p>\n

(2) \u4e00\u9636\u4e00\u81f4\u6027\u534f\u8bae<\/h5>\n

\u667a\u80fd\u4f53\u52a8\u6001\u6a21\u578b： [ \\\\dot{x}i(t) = -\\\\sum{j \\\\in \\\\mathcal{N}i} (x_i(t) – x_j(t)) ] \u76ee\u6807：\u6240\u6709 (x_i(t)) \u6536\u655b\u5230\u521d\u59cb\u72b6\u6001\u7684\u5747\u503c (\\\\bar{x} = \\\\frac{1}{N}\\\\sum{i=1}^N x_i(0)).<\/p>\n

% \u521d\u59cb\u72b6\u6001<\/span>
\nx0 =<\/span> [<\/span>3<\/span>;<\/span> –<\/span>1<\/span>;<\/span> 4<\/span>;<\/span> 0<\/span>;<\/span> 2<\/span>]<\/span>;<\/span> % \u6bcf\u4e2a\u667a\u80fd\u4f53\u7684\u521d\u59cb\u72b6\u6001<\/span><\/p>\n

% \u4eff\u771f\u53c2\u6570<\/span>
\ntspan =<\/span> [<\/span>0<\/span> 10<\/span>]<\/span>;<\/span> % \u65f6\u95f4\u8303\u56f4<\/span>
\ndt =<\/span> 0.01<\/span>;<\/span> % \u65f6\u95f4\u6b65\u957f<\/span><\/p>\n

% \u5b9a\u4e49\u52a8\u529b\u5b66\u65b9\u7a0b<\/span>
\nodefun =<\/span> @<\/span>(<\/span>t,<\/span> x)<\/span> –<\/span>L *<\/span> x;<\/span>
\n[<\/span>t,<\/span> x]<\/span> =<\/span> ode45<\/span>(<\/span>odefun,<\/span> tspan,<\/span> x0)<\/span>;<\/span><\/p>\n

% \u7ed8\u5236\u6536\u655b\u66f2\u7ebf<\/span>
\nfigure;<\/span>
\nplot<\/span>(<\/span>t,<\/span> x)<\/span>;<\/span>
\nxlabel<\/span>(<\/span>'Time (s)'<\/span>)<\/span>;<\/span>
\nylabel<\/span>(<\/span>'State x_i(t)'<\/span>)<\/span>;<\/span>
\ntitle<\/span>(<\/span>'\u4e00\u9636\u4e00\u81f4\u6027\u534f\u8bae\u6536\u655b\u8fc7\u7a0b'<\/span>)<\/span>;<\/span>
\ngrid on;<\/span><\/p>\n

\n

2. \u79bb\u6563\u65f6\u95f4\u4e00\u81f4\u6027\u534f\u8bae<\/h4>\n

\u82e5\u9700\u79bb\u6563\u65f6\u95f4\u6a21\u578b（\u5982\u901a\u4fe1\u95f4\u9694\u56fa\u5b9a）： [ x_i(k+1) = x_i(k) + \\\\epsilon \\\\sum_{j \\\\in \\\\mathcal{N}i} (x_j(k) – x_i(k)) ] \u5176\u4e2d (\\\\epsilon) \u4e3a\u6b65\u957f\u53c2\u6570（\u9700\u6ee1\u8db3 (0 < \\\\epsilon < 1\/\\\\Delta{\\\\text{max}})，(\\\\Delta_{\\\\text{max}}) \u4e3a\u6700\u5927\u8282\u70b9\u5ea6）\u3002<\/p>\n

% \u53c2\u6570\u8bbe\u7f6e<\/span>
\nepsilon =<\/span> 0.1<\/span>;<\/span> % \u9700\u6ee1\u8db3\u6536\u655b\u6761\u4ef6<\/span>
\nmax_iter =<\/span> 100<\/span>;<\/span> % \u6700\u5927\u8fed\u4ee3\u6b21\u6570<\/span><\/p>\n

% \u521d\u59cb\u5316<\/span>
\nx =<\/span> x0;<\/span>
\nx_history =<\/span> zeros<\/span>(<\/span>N,<\/span> max_iter+<\/span>1<\/span>)<\/span>;<\/span>
\nx_history<\/span>(<\/span>:<\/span>,<\/span> 1<\/span>)<\/span> =<\/span> x0;<\/span><\/p>\n

% \u79bb\u6563\u65f6\u95f4\u8fed\u4ee3<\/span>
\nfor<\/span> k =<\/span> 1<\/span>:<\/span>max_iter
\n x =<\/span> x –<\/span> epsilon *<\/span> L *<\/span> x;<\/span>
\n x_history<\/span>(<\/span>:<\/span>,<\/span> k+<\/span>1<\/span>)<\/span> =<\/span> x;<\/span>
\nend<\/span><\/p>\n

% \u7ed8\u5236\u7ed3\u679c<\/span>
\nfigure;<\/span>
\nplot<\/span>(<\/span>0<\/span>:<\/span>max_iter,<\/span> x_history'<\/span>)<\/span>;<\/span>
\nxlabel<\/span>(<\/span>'Iteration'<\/span>)<\/span>;<\/span>
\nylabel<\/span>(<\/span>'State x_i(k)'<\/span>)<\/span>;<\/span>
\ntitle<\/span>(<\/span>'\u79bb\u6563\u65f6\u95f4\u4e00\u81f4\u6027\u534f\u8bae\u6536\u655b\u8fc7\u7a0b'<\/span>)<\/span>;<\/span><\/p>\n

\n

3. \u542b\u9886\u5bfc\u8005\u7684\u5206\u5c42\u4e00\u81f4\u6027<\/h4>\n

\u5047\u8bbe\u5b58\u5728\u4e00\u4e2a\u9886\u5bfc\u8005（\u7f16\u53f7\u4e3a1），\u5176\u4ed6\u667a\u80fd\u4f53\u8ddf\u8e2a\u9886\u5bfc\u8005\u72b6\u6001： [ \\\\dot{x}i(t) = -\\\\sum{j \\\\in \\\\mathcal{N}i} (x_i – x_j) – b_i (x_i – x{\\\\text{leader}}) ] \u5176\u4e2d (b_i = 1) \u8868\u793a\u667a\u80fd\u4f53 (i) \u80fd\u76f4\u63a5\u63a5\u6536\u9886\u5bfc\u8005\u4fe1\u606f，\u5426\u5219 (b_i = 0).<\/p>\n

% \u5b9a\u4e49\u9886\u5bfc\u8005\u72b6\u6001（\u5047\u8bbe\u4e3a\u5e38\u6570）<\/span>
\nx_leader =<\/span> 5<\/span>;<\/span><\/p>\n

% \u6784\u5efa\u53cd\u9988\u77e9\u9635 B<\/span>
\nB =<\/span> diag<\/span>(<\/span>[<\/span>1<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>]<\/span>)<\/span>;<\/span> % \u53ea\u6709\u667a\u80fd\u4f531\u80fd\u89c2\u6d4b\u5230\u9886\u5bfc\u8005<\/span><\/p>\n

% \u4fee\u6539\u62c9\u666e\u62c9\u65af\u77e9\u9635\u4e3a L + B<\/span>
\nL_leader =<\/span> L +<\/span> B;<\/span><\/p>\n

% \u52a8\u529b\u5b66\u65b9\u7a0b<\/span>
\nodefun_leader =<\/span> @<\/span>(<\/span>t,<\/span> x)<\/span> –<\/span>L_leader *<\/span> x +<\/span> B *<\/span> x_leader *<\/span> ones<\/span>(<\/span>N,<\/span> 1<\/span>)<\/span>;<\/span>
\n[<\/span>t_leader,<\/span> x_leader_sim]<\/span> =<\/span> ode45<\/span>(<\/span>odefun_leader,<\/span> tspan,<\/span> x0)<\/span>;<\/span><\/p>\n

% \u7ed8\u5236\u7ed3\u679c<\/span>
\nfigure;<\/span>
\nplot<\/span>(<\/span>t_leader,<\/span> x_leader_sim)<\/span>;<\/span>
\nhold on;<\/span>
\nplot<\/span>(<\/span>t_leader,<\/span> x_leader*<\/span>ones<\/span>(<\/span>size<\/span>(<\/span>t_leader)<\/span>)<\/span>,<\/span> 'k–'<\/span>,<\/span> 'LineWidth'<\/span>,<\/span> 2<\/span>)<\/span>;<\/span>
\ntitle<\/span>(<\/span>'\u542b\u9886\u5bfc\u8005\u7684\u5206\u5c42\u4e00\u81f4\u6027'<\/span>)<\/span>;<\/span>
\nlegend<\/span>(<\/span>'Agent 1'<\/span>,<\/span> 'Agent 2'<\/span>,<\/span> 'Agent 3'<\/span>,<\/span> 'Agent 4'<\/span>,<\/span> 'Agent 5'<\/span>,<\/span> 'Leader'<\/span>)<\/span>;<\/span><\/p>\n

\n

4. \u65f6\u53d8\u62d3\u6251\u4e00\u81f4\u6027<\/h4>\n

\u6a21\u62df\u52a8\u6001\u53d8\u5316\u7684\u7f51\u7edc\u62d3\u6251（\u5982\u968f\u673a\u5207\u6362\u7684\u901a\u4fe1\u94fe\u8def）：<\/p>\n

% \u751f\u6210\u4e24\u4e2a\u4e0d\u540c\u7684\u62d3\u6251（\u793a\u4f8b：\u73af\u5f62\u548c\u661f\u578b）<\/span>
\nA1 =<\/span> A;<\/span> % \u73af\u5f62\u62d3\u6251（\u4e4b\u524d\u7684\u90bb\u63a5\u77e9\u9635）<\/span>
\nA2 =<\/span> [<\/span>0<\/span> 1<\/span> 1<\/span> 1<\/span> 1<\/span>;<\/span> % \u661f\u578b\u62d3\u6251（\u4e2d\u5fc3\u8282\u70b91）<\/span>
\n 1<\/span> 0<\/span> 0<\/span> 0<\/span> 0<\/span>;<\/span>
\n 1<\/span> 0<\/span> 0<\/span> 0<\/span> 0<\/span>;<\/span>
\n 1<\/span> 0<\/span> 0<\/span> 0<\/span> 0<\/span>;<\/span>
\n 1<\/span> 0<\/span> 0<\/span> 0<\/span> 0<\/span>]<\/span>;<\/span>
\nL1 =<\/span> diag<\/span>(<\/span>sum<\/span>(<\/span>A1,<\/span>2<\/span>)<\/span>)<\/span> –<\/span> A1;<\/span>
\nL2 =<\/span> diag<\/span>(<\/span>sum<\/span>(<\/span>A2,<\/span>2<\/span>)<\/span>)<\/span> –<\/span> A2;<\/span><\/p>\n

% \u5b9a\u4e49\u65f6\u53d8\u62d3\u6251\u51fd\u6570（\u6bcf2\u79d2\u5207\u6362\u4e00\u6b21）<\/span>
\nL_time_varying =<\/span> @<\/span>(<\/span>t)<\/span> (<\/span>mod<\/span>(<\/span>t,<\/span>4<\/span>)<\/span> <<\/span> 2<\/span>)<\/span> *<\/span> L1 +<\/span> (<\/span>mod<\/span>(<\/span>t,<\/span>4<\/span>)<\/span> >=<\/span> 2<\/span>)<\/span> *<\/span> L2;<\/span><\/p>\n

% \u52a8\u529b\u5b66\u65b9\u7a0b（\u4f7f\u7528ode45）<\/span>
\nodefun_tv =<\/span> @<\/span>(<\/span>t,<\/span> x)<\/span> –<\/span>L_time_varying<\/span>(<\/span>t)<\/span> *<\/span> x;<\/span>
\n[<\/span>t_tv,<\/span> x_tv]<\/span> =<\/span> ode45<\/span>(<\/span>odefun_tv,<\/span> tspan,<\/span> x0)<\/span>;<\/span><\/p>\n

% \u7ed8\u5236\u7ed3\u679c<\/span>
\nfigure;<\/span>
\nplot<\/span>(<\/span>t_tv,<\/span> x_tv)<\/span>;<\/span>
\ntitle<\/span>(<\/span>'\u65f6\u53d8\u62d3\u6251\u4e0b\u7684\u4e00\u81f4\u6027\u6536\u655b'<\/span>)<\/span>;<\/span><\/p>\n

\n

5. \u6536\u655b\u6027\u5206\u6790<\/h4>\n

(1) \u7406\u8bba\u9a8c\u8bc1<\/h5>\n