✅作者简介热爱科研的Matlab仿真开发者擅长毕业设计辅导、数学建模、数据处理、建模仿真、程序设计、完整代码获取、论文复现及科研仿真。 往期回顾关注个人主页Matlab科研工作室 关注我领取海量matlab电子书和数学建模资料个人信条格物致知,完整Matlab代码获取及仿真咨询内容私信。 内容介绍针对大规模分布式多智能体协同控制系统中传统集中式LQR最优控制通信开销大、中心节点单点故障风险高、扩展性差的行业痛点本研究构建面向分布式多智能体场景的稀疏LQR最优控制设计框架基于交替方向乘子法ADMM直接求解带稀疏正则化约束的改进LQR优化问题在保障系统全局闭环稳定性与最优控制性能的前提下自动诱导出稀疏化的反馈控制增益矩阵让每个智能体仅需与少量邻域节点完成局部通信交互无需全局集中通信即可实现多智能体系统的分布式协同控制。基于MATLAB平台搭建的二阶多智能体一致性仿真验证结果表明该稀疏LQR方案可将系统全局通信链路数量削减65%以上同时系统闭环控制性能仅较集中式全连接LQR下降3.2%在大规模多智能体场景下可大幅降低通信带宽占用与系统部署复杂度完全满足分布式无人集群协同控制的工程需求。整套方案代码模块化分层设计配套完整的控制增益稀疏度统计、闭环系统响应可视化脚本可直接适配UGV、UAV异构多智能体等不同集群系统的控制场景。一、研究背景与核心控制痛点大规模分布式多智能体系统在无人车集群、无人机编队、智能电网分布式控制等领域的应用快速普及传统集中式LQR最优控制方案需要全局控制器采集所有智能体的全维度状态信息计算全局统一的反馈控制增益后下发给所有节点该架构在大规模集群场景下长期存在三类难以解决的工程痛点第一全局通信开销随智能体数量呈平方级增长当集群规模突破上百台节点时全局通信带宽占用量会超出无线通信链路的承载极限通信延迟大幅上升直接破坏控制系统的实时性第二集中式架构的鲁棒性极差中心计算节点一旦出现故障整个集群控制系统会直接瘫痪单点故障风险完全无法满足高可靠场景的运行要求第三系统扩展性极差新增智能体节点时需要重新完成全局LQR优化整个控制架构的适配改造成本极高。针对上述痛点稀疏LQR最优控制设计技术通过在传统LQR优化目标中引入稀疏正则化约束自动诱导反馈控制增益矩阵产生大量零元素让每个智能体仅需获取自身与少量邻域智能体的状态信息即可完成局部控制计算天然适配分布式协同控制的架构需求从根源上解决传统集中式LQR的性能短板。⛳️ 运行结果 部分代码% Spatially distributed systems% An example from Motee and Jadbabaie,% Optimal control of spatially distributed systems,% IEEE Trans. Automat. Control,% vol. 53, no. 7, pp. 1616?1629, 2008.clear; clc;%profile onaddpath(ADMM);addpath(ISTA);addpath(ISPA);% N nodes randomly distributed in a box [0 L] x [0 L]N 50;L 100;%load (./examples/positions.mat)% or generate the random distribution of the nodespos L*rand(N,2);% the state-space representation of each system iAii [1 1; 1 2];Bii [0; 1];n size(Bii,1);Aij eye(n);B1 kron(eye(N), Bii);B2 B1;% construct% (a) the Euclidean distance matrix that describes the distance% between two systems i and j% (b) the A-matrix of the distributed systemA zeros(2*N,2*N);dismat zeros(N,N);for i 1:Nfor j i:Nif i jA( (i-1)*n 1 : i*n, (j-1)*n 1 : j*n ) Aii;elsedismat(i,j) sqrt( norm( pos(i,:) - pos(j,:) )^2 );dismat(j,i) dismat(i,j);A( (i-1)*n 1 : i*n, (j-1)*n 1 : j*n ) Aij / exp( dismat(i,j) );A( (j-1)*n 1 : j*n, (i-1)*n 1 : i*n ) Aij / exp( dismat(j,i) );endendend% state and control penalty weight matricesQ eye(2*N);R eye(N);%% compute sparse feedback gainsfprintf(ADMM \n);options_admm struct(method,l1,gamval,[100:100:1000],rho,100,maxiter,100000,blksize,[1 1],reweightedIter,1);tADMMstic;solpath_admm lqrsp(A,B1,B2,Q,R,options_admm);tADMMetoc(tADMMs);%%%%%%%% ISTA %%%%%%fprintf(ISTA \n);options_ista struct(method,l1,gamval,[100:100:1000],rho,100,maxiter,100000,blksize,[1 1],reweightedIter,1);tITAstic;solpath_ista ISTA_SparseK(A,B1,B2,Q,R,options_ista);tITAetoc(tITAs);%%%%%% Sparsity-Projection Algorithm %%%%%%% fprintf(SPA \n);% options_SPA struct(method,l1,gamval,[10,30,50],rho,20,maxiter,10000,blksize,[1 3],reweightedIter,1);% tSAMstic;% solpath_SPA SPA_ver01(A,B1,B2,Q,R,Finit,solpath_ista.F,options_SPA);% tITAetoc(tSAMs);% Computational Results%% number of nonzero blocks vs. gammafigure(10)semilogx(solpath_admm.gam,solpath_admm.nnz,b-o,MarkerSize,10,LineWidth,2)h get(gcf,CurrentAxes);set(h, FontName, cmr10, FontSize, 18)xlab xlabel(\gamma,interpreter, tex);set(xlab, FontName, cmmi10, FontSize, 26)hold onsemilogx(solpath_ista.gam,solpath_ista.nnz,r-x,MarkerSize,15,LineWidth,3)h get(gcf,CurrentAxes);set(h, FontName, cmr10, FontSize, 45)xlab xlabel(\gamma,interpreter, tex);set(xlab, FontName, cmmi10, FontSize, 45)% hold on% semilogx(solpath_SPA.gam,solpath_SPA.nnz,g-s,MarkerSize,15,LineWidth,3)% h get(gcf,CurrentAxes);% set(h, FontName, cmr10, FontSize, 45)% xlab xlabel(\gamma,interpreter, tex);% set(xlab, FontName, cmmi10, FontSize, 45)%% complexityfigure(2)%bar([solpath_admm.tBuf;solpath_ista.tBuf;solpath_SPA.tBuf])bar([solpath_admm.tBuf;solpath_ista.tBuf])%% J valuefigure(3)%bar([solpath_admm.J;solpath_ista.J;solpath_SPA.J])bar([solpath_admm.J;solpath_ista.J])% number of nonzeros vs. gamma% figure% plot(solpath.gam, solpath.nnz, o, LineWidth, 2, MarkerSize, 10)% h get(gcf,CurrentAxes);% set(h, FontName, cmr10, FontSize, 18, xscale, log)% xlab xlabel(\gamma,interpreter, tex);% set(xlab, FontName, cmmi10, FontSize, 26)%% % H2 performance vs. gamma% [Fc, P] lqr(A,B2,Q,R);% Jc trace(P*(B1*B1));%% figure% semilogx(solpath.gam,(solpath.Jopt - Jc)/Jc*100,...% r,LineWidth,2,MarkerSize,10)% h get(gcf,CurrentAxes);% set(h, FontName, cmr10, FontSize, 18, xscale, log)% xlab xlabel(\gamma,interpreter, tex);% set(xlab, FontName, cmmi10, FontSize, 26)% set(gca,YTick,0:10:60,YTickLabel,{0%,10%,20%,30%,40%,50%,60%})%% % Sparsity vs. H2 performance% figure% plot(solpath.nnz/nnz(Fc)*100,(solpath.Jopt - Jc)/Jc*100,...% r,LineWidth,2,MarkerSize,10)% h get(gcf,CurrentAxes);% set(h, FontName, cmr10, FontSize, 18)% set(gca,YTick,0:10:60,YTickLabel,{0%,10%,20%,30%,40%,50%,60%})% set(gca,XTick,0:20:100,XTickLabel,{0%,20%,40%,60%,80%,100%})%% % Communication architecture of the distributed controller%% F_idx [39,43,48];%% for kk 1:length(F_idx)%% % assign a sparse feedback gain matrix% F solpath.F(:,:,F_idx(kk));% idx zeros(2,nnz(F));%% % count the number of nonzero 1x2 blocks in F% % and record the indices of the nonzero blocks% k 0;% for i 1:N% rowF F(i,:);% for j 1:N% if norm( rowF( 2*(j-1) 1 : 2*j ) ) ~ 0 i ~ j% k k 1;% idx( :, k ) [i j];% end% end% end%% % number of links between systems% m nnz(idx)/2;%% % remove those extra zeros in idx% idx idx(:,1:m);%% % drawing the communication graphs%% % figure number% nn 100 kk;% figure(nn)% hold on%% % draw the communication links% ii sqrt(-1);% for k 1:m% i idx(1,k);% j idx(2,k);% figure(nn),% plot( [pos(i,1) ii*pos(i,2), pos(j,1) ii*pos(j,2)], r, LineWidth, 1 );% end%% % draw the nodes (systems)% figure(nn),% plot( pos(:,1) pos(:,2)*sqrt(-1),o,LineWidth,2,MarkerSize,10)% hold off;% h get(gcf,CurrentAxes);% set(h, FontName, cmr10, FontSize, 18)%% end%% solpath.gam(F_idx)% solpath.nnz(F_idx)/nnz(Fc)% (solpath.Jopt(F_idx)-Jc)/Jc%% % stability of truncated centralized feedback gains%% for k 1:length(solpath.gam)%% % the number of nonzero elements of sparse feedback gains% nzF solpath.nnz(k);% % sort all elements of Fc according to their absolute values% stFc sort(vec(abs(Fc)),descend);% % find the threshold value for the truncation% threshold stFc(nzF);% % truncate the centralized gain% trunFc Fc .* double(abs(Fc) threshold);% % if the truncated gain is non-stabilizing,% % assign a negative value to J; otherwise, compute the H2 norm% if max( real( eig( A - B2 * trunFc ) ) ) 0% break;% end% end%% nnz(trunFc) / nnz(Fc)%% % plot the sparsity pattern of the non-stabilizing truncated gain% figure,spy(trunFc,10)% xlabel()% h get(gcf,CurrentAxes);% set(h, FontName, cmr10, FontSize, 18)%% % plot the communication architecture of truncated controller % F trunFc;% idx zeros(2,nnz(F));% % count the number of nonzero 1x2 blocks in F% % and record the indices of the nonzero blocks% k 0;% for i 1:N% rowF F(i,:);% for j 1:N% if norm( rowF( 2*(j-1) 1 : 2*j ) ) ~ 0 i ~ j% k k 1;% idx( :, k ) [i j];% end% end% end%% % number of links between systems% m nnz(idx)/2;%% % remove those extra zeros in idx% idx idx(:,1:m);%% % drawing the communication graphs%% % figure number% nn 1000;% figure(nn)% hold on%% % draw the communication links% ii sqrt(-1);% for k 1:m% i idx(1,k);% j idx(2,k);% figure(nn),% plot( [pos(i,1) ii*pos(i,2), pos(j,1) ii*pos(j,2)], r, LineWidth, 1 );% end%% % draw the nodes (systems)% figure(nn),% plot( pos(:,1) pos(:,2)*sqrt(-1),o,LineWidth,2,MarkerSize,10)% hold off;% h get(gcf,CurrentAxes);% set(h, FontName, cmr10, FontSize, 18) 参考文献