【多智能体】指定性能约束的动态、领导者-跟随者交互以及 MFASMC 算法的Matlab实现。

✅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、算法改进、程序设计科研仿真。完整代码获取 定制创新 论文复现私信个人信条做科研博学之、审问之、慎思之、明辨之、笃行之是为博学慎思明辨笃行。1. 相关介绍指定性能约束的动态原理指定性能约束动态主要基于预设性能控制PPC。其核心是通过设计性能函数对跟踪误差的收敛轨迹进行限制确保系统误差始终位于动态变化的上下限之间从而实现对控制系统动态性能的约束与调节。例如通过设计可指定收敛时间的性能函数结合自适应项调整误差包络能在保证理想控制精度的同时兼顾超调和调节时间等动态性能使控制系统具有较好的过渡品质。领导者 - 跟随者交互原理在多智能体系统中领导者 - 跟随者模式是一种常见的协作方式。领导者通常根据环境信息或任务要求生成行动策略或轨迹。跟随者则通过感知领导者的状态如位置、速度等调整自身行为以实现与领导者的协同运动或达到特定的群体目标。这种交互方式可基于多种机制如基于规则的交互跟随者遵循预设规则来模仿或跟随领导者也可基于学习的方式跟随者通过强化学习等算法从与领导者的交互中学习最优策略。MFASMC 算法背景原理MFASMC 即无模型自适应滑模控制算法其背景是针对一些系统难以建立精确数学模型且传统基于模型的控制策略存在控制律复杂、参数调节繁琐、通用性差等问题而提出的。该算法基于梯度法设计自适应参数调节律利用滑模控制响应快、鲁棒性好的特点通过设计控制器参数的调节规律可实现对控制参数的快速在线调节避免了繁杂的数学建模过程及控制参数调节过程对于不同特性的对象具有良好的适应性及通用性。2. 运行效果展示3. 部分代码呈现clc; clear;%Parametersrho 10.5;eta 5;lamda 120;mu 80.5;epsilon 1e-5;alpha 1;T 0.1;gamma1 0.05;gamma2 0.05;gamma3 0.05;gamma4 0.05;beta 10;sigma 95;tau 1e-5;nena 1e-5;rT 1024;L 200;m 500;n 600;% initializationphi1 zeros(m1, 1);phi2 zeros(m1, 1);phi3 zeros(m1, 1);phi4 zeros(m1, 1);mfa1 zeros(m1, 1);mfa2 zeros(m1, 1);mfa3 zeros(m1, 1);mfa4 zeros(m1, 1);sm1 zeros(m,1);sm2 zeros(m,1);sm3 zeros(m,1);sm4 zeros(m,1);y1 zeros(m1, 1);y2 zeros(m1, 1);y3 zeros(m1, 1);y4 zeros(m1, 1);u1 zeros(m,1);u2 zeros(m,1);u3 zeros(m,1);u4 zeros(m,1);xi1 zeros(m, 1);xi2 zeros(m, 1);xi3 zeros(m, 1);xi4 zeros(m, 1);s1 zeros(m, 1);s2 zeros(m, 1);s3 zeros(m, 1);s4 zeros(m, 1);omega1 zeros(m, 1);omega2 zeros(m, 1);omega3 zeros(m, 1);omega4 zeros(m, 1);%Time Invarying Leaders signals (w5, w6)% Preallocate arrays (adjust size if needed)w5 zeros(1, m); % example length, adjust as neededw6 zeros(1, m); % example length, adjust as needed% Set w5 values according to conditionsw5(1:165) 1.4;w5(166:330) 1.6;w5(331:end) 1.1;% Set w6 values according to conditionsw6(1:165) 0.7;w6(166:330) 1.2;w6(331:end) 0.8;% Variation 1: Low-frequency, same amplitude, phase-shifted signals% % Time vector for sinusoidal signals% k 1:m;% t (k-1) * T; % Time vector: t (k-1)*T% % Define sinusoidal leader signals (choose one of the variations below)% % Variation 1: Low-frequency, same amplitude, phase-shifted signals% w5 0.5 0.25 * sin(0.1 * t); % Amplitude 0.25, frequency 0.1 rad/s, offset 1.15% w6 0.5 0.25 * sin(0.1 * t pi/2); % Same amplitude and frequency, phase shift pi/2for k 1:mif k 1phi1(k) 1;phi2(k) 1;phi3(k) 1;phi4(k) 1;elseif k 2phi1(k) phi1(k-1) (eta * u1(k-1) / (mu u1(k-1)^2)) * (y1(k) - phi1(k-1)*u1(k-1));phi2(k) phi2(k-1) (eta * u2(k-1) / (mu u2(k-1)^2)) * (y2(k) - phi2(k-1)*u2(k-1));phi3(k) phi3(k-1) (eta * u3(k-1) / (mu u3(k-1)^2)) * (y3(k) - phi3(k-1)*u3(k-1));phi4(k) phi4(k-1) (eta * u4(k-1) / (mu u4(k-1)^2)) * (y4(k) - phi4(k-1)*u4(k-1));elsephi1(k) phi1(k-1) (eta * (u1(k-1) - u1(k-2)) / (mu (u1(k-1) - u1(k-2))^2)) * (y1(k) - y1(k-1) - phi1(k-1) * (u1(k-1) - u1(k-2)));phi2(k) phi2(k-1) (eta * (u2(k-1) - u2(k-2)) / (mu (u2(k-1) - u2(k-2))^2)) * (y2(k) - y2(k-1) - phi2(k-1) * (u2(k-1) - u2(k-2)));phi3(k) phi3(k-1) (eta * (u3(k-1) - u3(k-2)) / (mu (u3(k-1) - u3(k-2))^2)) * (y3(k) - y3(k-1) - phi3(k-1) * (u3(k-1) - u3(k-2)));phi4(k) phi4(k-1) (eta * (u4(k-1) - u4(k-2)) / (mu (u4(k-1) - u4(k-2))^2)) * (y4(k) - y4(k-1) - phi4(k-1) * (u4(k-1) - u4(k-2)));end% Stability protectionif k 2 (abs(phi1(k)) epsilon || abs(u1(k - 1) - u1(k - 2)) epsilon || sign(phi1(k)) ~ sign(phi1(1)))phi1(k) phi1(1);endif k 2 (abs(phi2(k)) epsilon || abs(u2(k - 1) - u2(k - 2)) epsilon || sign(phi2(k)) ~ sign(phi2(1)))phi2(k) phi2(1);endif k 2 (abs(phi3(k)) epsilon || abs(u3(k - 1) - u3(k - 2)) epsilon || sign(phi3(k)) ~ sign(phi3(1)))phi3(k) phi3(1);endif k 2 (abs(phi4(k)) epsilon || abs(u4(k - 1) - u4(k - 2)) epsilon || sign(phi4(k)) ~ sign(phi4(1)))phi4(k) phi4(1);end% Example for one time step:xi1(k) y2(k) - 2 * y1(k) w5(k);xi2(k) y3(k) - y2(k);xi3(k) y4(k) - 2 * y3(k) y1(k);xi4(k) y2(k) - 2 * y4(k) w6(k);% Fix: Handle k1 case for sliding surfacesif k 1s1(k) 0;s2(k) 0;s3(k) 0;s4(k) 0;elses1(k) alpha * xi1(k) - xi1(k-1);s2(k) alpha * xi2(k) - xi2(k-1);s3(k) alpha * xi3(k) - xi3(k-1);s4(k) alpha * xi4(k) - xi4(k-1);end% Fix: Handle k1 case for sliding surfacesif k 1omega1(k) 0;omega2(k) 0;omega3(k) 0;omega4(k) 0;elseomega1(k) s1(k) tau * (s1(k-1));omega2(k) s2(k) tau * (s2(k-1));omega3(k) s3(k) tau * (s3(k-1));omega4(k) s4(k) tau * (s4(k-1));endif k 1mfa1(k) 0;mfa2(k) 0;mfa3(k) 0;mfa4(k) 0;elsemfa1(k) mfa1(k-1) (rho * phi1(k)) / (lamda abs(phi1(k)^2)) * xi1(k);mfa2(k) mfa2(k-1) (rho * phi2(k)) / (lamda abs(phi2(k)^2)) * xi2(k);mfa3(k) mfa3(k-1) (rho * phi3(k)) / (lamda abs(phi3(k)^2)) * xi3(k);mfa4(k) mfa4(k-1) (rho * phi4(k)) / (lamda abs(phi4(k)^2)) * xi4(k);end% SMC updatesif k 1sm1(k) 0;sm2(k) 0;sm3(k) 0;sm4(k) 0;elsesm1(k) sm1(k-1) (beta * phi1(k)) / (sigma (phi1(k))^2) * ...( (xi1(k) (y4(k) - y4(k-1)) (w5(k) - w5(k-1))(w6(k) - w6(k-1))) / (1 1) ... (1-tau * alpha) * xi1(k) - tau * xi1(k-1) / (alpha * (2)) nena * sign(omega1(k)) );sm2(k) sm2(k-1) (beta * phi2(k)) / (sigma (phi2(k))^2) * ...( (xi2(k) (y3(k) - y3(k-1)) (w5(k) - w5(k-1))(w6(k) - w6(k-1))) / (1) ... (1-tau * alpha) * xi2(k) - tau * xi2(k-1) / (alpha * (1)) nena * sign(omega2(k)) );sm3(k) sm3(k-1) (beta * phi3(k)) / (sigma (phi3(k))^2) * ...( (xi3(k) (y1(k) - y1(k-1)) (y4(k) - y4(k-1)) (w5(k) - w5(k-1))(w6(k) - w6(k-1))) / (2) ... (1-tau * alpha) * xi3(k) - tau * xi3(k-1) / (alpha * (2)) nena * sign(omega3(k)) );sm4(k) sm4(k-1) (beta * phi4(k)) / (sigma (phi4(k))^2) * ...( (xi4(k) (y2(k) - y3(k-1)) (w5(k) - w5(k-1))(w6(k) - w6(k-1))) / (2) ... (1-tau * alpha) * xi4(k) - tau * xi4(k-1) / (alpha * (2)) nena * sign(omega4(k)) );end% Control signalif k 1u1(k) 0;u2(k) 0;u3(k) 0;u4(k) 0;elseu1(k) mfa1(k) gamma1 * sm1(k);u2(k) mfa2(k) gamma2 * sm2(k);u3(k) mfa3(k) gamma3 * sm3(k);u4(k) mfa4(k) gamma4 * sm4(k);endif k 1y1(k) 0;y2(k) 0;y3(k) 0;y4(k) 0;end% System dynamics (example, replace with actual system equations)y1(k 1) m / (rT * 0.1) * u1(k);y2(k 1) m / (rT * 0.1) * u2(k);y3(k 1) m / (rT * 0.1) * u3(k);y4(k 1) m / (rT * 0.3) * u4(k);% Ensure y values do not exceed bounds (example, adjust as needed)% y1(k) max(0, min(1, y1(k)));% y2(k) max(0, min(1, y2(k)));% y3(k) max(0, min(1, y3(k)));% y4(k) max(0, min(1, y4(k)));% % Ensure u values do not exceed bounds (example, adjust as needed)% u1(k) max(0, min(1, u1(k)));% u2(k) max(0, min(1, u2(k)));% u3(k) max(0, min(1, u3(k)));% u4(k) max(0, min(1, u4(k)));% % Ensure phi values do not exceed bounds (example, adjust as needed)% phi1(k) max(0, min(1, phi1(k)));% phi2(k) max(0, min(1, phi2(k)));% phi3(k) max(0, min(1, phi3(k)));% phi4(k) max(0, min(1, phi4(k)));% Plottingend% Time vectork 1:m;% Create a main figure windowfigure(Position, [100, 100, 1000, 550]);% Define zoom range (adjust as needed)zoomStart 400;zoomEnd m;zoomed_fontsize 20;font_size 20;font_family Times New Roman;% Agent 1% subplot(2,2,1);% Combined Containment Error Plot for All Agents plot(k, xi1(1:m), b, LineWidth, 2); hold on;plot(k, xi2(1:m), r, LineWidth, 2);plot(k, xi3(1:m), g, LineWidth, 2);plot(k, xi4(1:m), m, LineWidth, 2);% Main labels and title% title(Containment Errors of All Agents, FontSize, font_size, FontName, font_family);xlabel(Time step (k), FontSize, font_size, FontName, font_family);ylabel(Containment error, FontSize, font_size, FontName, font_family);% Legendlegend({\Xi_1(k), \Xi_2(k), \Xi_3(k), \Xi_4(k)}, ...FontSize, font_size, FontName, font_family,Location, north, Orientation, horizontal);grid off;set(gca, FontSize, font_size, FontName, font_family);% Zoomed Inset (for all agents in the same zoom window) axes(Position, [0.45 0.50 0.30 0.25]); % inset positionbox on; hold on;plot(k(zoomStart:zoomEnd), xi1(zoomStart:zoomEnd), b, LineWidth, 1.2);plot(k(zoomStart:zoomEnd), xi2(zoomStart:zoomEnd), r, LineWidth, 1.2);plot(k(zoomStart:zoomEnd), xi3(zoomStart:zoomEnd), g, LineWidth, 1.2);plot(k(zoomStart:zoomEnd), xi4(zoomStart:zoomEnd), m, LineWidth, 1.2);% ylim([-0.05 0.05]); % adjust depending on your dataset(gca, FontSize, zoomed_fontsize, FontName, font_family);% title(Zoomed View, FontSize, zoomed_fontsize, FontName, font_family);​4. 参考文献更多免费数学建模和仿真教程关注领取如果觉得内容不错那就请分享和点个“在看”呗