✅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。 内容介绍本文探讨了最优时不变编队跟踪问题旨在为具有二阶积分器动力学特性的多智能体系统提供分布式解决方案。在相关文献中大多数关于多智能体编队跟踪的研究在探究分布式反馈控制律时并未考虑能量问题。为解决这一关键设计要点我们通过在优化成本中精心选择特定且关键的势函数对一个涵盖轨迹跟踪、基于距离的编队控制以及输入能量最小化的优化问题进行了形式化处理并给出解决方案以此做出贡献。为此我们展示了如何借助基于投影算子的轨迹优化牛顿法PRONTO以集中式方式计算逆动力学。更重要的是我们将这种离线解决方案作为通用参考来设计一种稳定的在线分布式控制律。最后给出了涉及三维空间中沿直线路径的立方体编队的数值示例以验证所提出的控制策略。⛳️ 运行结果 部分代码close allclear all, clc​global dt nAg M kr ka QBp QBdp R kF kA Xdes dijs G flag33 flag50 flag90​dt 0.01;tl 200;T0 (0:dt:tl);T length(T0);​nAg 4;I_nAg eye(nAg);M 2;I_M eye(M);​QBp 10^1;QBdp 10^1;R 10^0;kF 10^0;kA 5*10^-1;kr 1;ka 50;​% initial conditionsvel 1;x0p [-2 1 -3 -1 2 -2 0 0];x0p x0p/(2*norm(x0p));x0p rand(1,8)*10;x0v 5*[0 -vel 0 -vel 0 -vel 0 -vel];​% desired trajectory for the centroidxd0p zeros(1,M);xd0v 1*[vel 0];Xdesp repmat(xd0p,length(T0),1) T0*xd0v;Xdesv repmat(xd0v,length(T0),1);Xdes [ Xdesp Xdesv ];​% framework definitiondist_coeff 1.05;dd 5;% dijs [0 dd dd;% dd 0 dd;% dd dd 0];dd1_2 sqrt(2)*dd;max_dijs dd1_2;INF epsdist_coeff*dd1_2;dijs [0 dd INF dd;dd 0 dd dd1_2;INF dd 0 dd;dd dd1_2 dd 0];​A zeros(nAg);for i 1:nAgfor j 1:i-1if dijs(i,j) 0A(i,j) 1;A(j,i) 1;endendendG graph(A);degs sum(A);D diag(degs);L D-A;L_ D^(-1/2)*L*D^(-1/2);eigsL_ sort(eig(L_));lambda1 eigsL_(2);lambdan_1 eigsL_(end);muL_ (lambda1lambdan_1)/2;eta_star 1-1/muL_;if eta_star 0eta_star 0;end% if topology remains constant:F eye(nAg)*eta_star(D^-1*A)*(1-eta_star);​​%% -------------------------------------------------------% parametersparams.dt dt;params.nAg nAg;params.M M;params.QBp QBp;params.QBdp QBdp;params.R R;params.kF kF;params.kA kA;params.Xdes Xdes;params.dijs dijs;params.G G;params.tl tl;params.F kron(F,I_M);params.dist_coeff dist_coeff;params.max_dist max_dijs; % max(dijs(:));​% flags to show completionflag33 0;flag50 0;flag90 0;​% dynamics integration[t,x_history] ode45((t,x)distr_dyn(t,x,params),T0,[x0p x0v]);​​%% display final resultsfinal_state x_history(end,:);disp(final_state)p1 x_history(end,1:2)p2 x_history(end,3:4)p3 x_history(end,5:6)p4 x_history(end,7:8)e12 p1-p2;e13 p1-p3;e23 p2-p3;e14 p1-p4;e24 p2-p4;e34 p3-p4;pB (p1p2p3p4)/4Ne12 norm(e12)Ne13 norm(e13)Ne23 norm(e23)Ne14 norm(e14)Ne24 norm(e24)Ne34 norm(e34)​​%% fase diagram for positions​​​figuregrid onhold onplot(Xdes(:,1),Xdes(:,2),k)for i 1:nAgplot(x_history(:,(i-1)*M1),x_history(:,(i-1)*M2),r)endfor i 1:nAgplot(x_history(end,(i-1)*M1),x_history(end,(i-1)*M2),b*,linewidth,3)end% inserire qui un confronto tra grafici... prendere i dati altrui potrebbe% essere una buona idea per poi plottare la traiettoria distribuita su% quella centralizzata - fare un esempio con triangolo equilatero% - traiettoria% - funzionale di costo% - input speso% - ripartizione tra formation vs tracking% * consensus solo per il distribuito% nota: mettere il peso finale per la final boundary condition nel caso% centralizzato!! (peso finale appropriato, no un punto a caso per la% traiettoria desiderata)axis equal​%% evolutions of the distance errors (sigma_dij-s)​figuregrid onhold ondist_errors zeros(T,nAg*(nAg-1)/2);​k 0;for i 2:nAgfor j 1:i-1dij dijs(i,j);if dij 0for tt 1:Tp_i_t x_history(tt,(i-1)*M1:(i-1)*MM);p_j_t x_history(tt,(j-1)*M1:(j-1)*MM);sij_t norm(p_i_t-p_j_t)^2;dist_errors(tt,k1) sigma(sij_t,dij,0);endelsedist_errors(:,k1) -ones(T,1);endk k1;endend​k 0;for i 2:nAgfor j 1:i-1tratto -;if dijs(i,j) 0tratto --;endplot(T0,dist_errors(:,k1),tratto,linewidth,1.5)k k1;endend​title(zero-order consensus)xlabel($t$,interpreter,latex)ylabel($\sigma(s_{ij})\qquad$,interpreter,latex)set(gca,fontsize,25)set(get(gca,ylabel),rotation,0)​​%% evolutions of the first derivatives of the distance errors (sigma_dij-s)​figuregrid onhold onddist_errors zeros(T,nAg*(nAg-1)/2);​k 0;for i 2:nAgfor j 1:i-1dij dijs(i,j);if dij 0for tt 1:Tp_i_t x_history(tt,(i-1)*M1:(i-1)*MM);p_j_t x_history(tt,(j-1)*M1:(j-1)*MM);sij_t norm(p_i_t-p_j_t)^2;ddist_errors(tt,k1) sigma(sij_t,dij,1);endelseddist_errors(:,k1) zeros(T,1);endk k1;endend​k 0;for i 2:nAgfor j 1:i-1tratto -;if dijs(i,j) 0tratto --;endplot(T0,ddist_errors(:,k1),tratto,linewidth,1.5)k k1;endend​title(first-order consensus)xlabel($t$,interpreter,latex)ylabel($\frac{\partial\sigma}{\partial s_{ij}}\qquad$,interpreter,latex)set(gca,fontsize,25)set(get(gca,ylabel),rotation,0)​%% evolutions of the second derivatives of the distance errors (sigma_dij-s)​figuregrid onhold ondddist_errors zeros(T,nAg*(nAg-1)/2);​k 0;for i 2:nAgfor j 1:i-1dij dijs(i,j);if dij 0for tt 1:Tp_i_t x_history(tt,(i-1)*M1:(i-1)*MM);p_j_t x_history(tt,(j-1)*M1:(j-1)*MM);sij_t norm(p_i_t-p_j_t)^2;dddist_errors(tt,k1) sigma(sij_t,dij,2);endelsedddist_errors(:,k1) zeros(T,1);endk k1;endend​k 0;for i 2:nAgfor j 1:i-1tratto -;if dijs(i,j) 0tratto --;endplot(T0,dddist_errors(:,k1),tratto,linewidth,1.5)k k1;endend​title(second-order consensus)xlabel($t$,interpreter,latex)ylabel($\frac{\partial^2\sigma}{\partial s_{ij}^2}\qquad$,interpreter,latex)set(gca,fontsize,25)set(get(gca,ylabel),rotation,0) 参考文献往期回顾扫扫下方二维码