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main.asv
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%file: main.m
global n %采样点个数
global det_L %各段路程（斜边） 数组
global alpha %各位置坡度角 数组
global beta %各位置迎风角 数组
global miu %各位置滚动摩擦因数 数组
global rho %各位置斜坡曲率 数组
global r %各位置弯道曲率 数组
global vw %风速
global M %质量
global g %重力加速度
global K %计算空气阻力的系数
global W %初始能量
global CP %临界功率
global vmax %人体机能提供速度上限
global vlimit %各位置弯道速度限制 数组
global V0 %迭代初始速度数组
global v0 %初始速度
global L %路程总长（斜边）
global x_L %采样点 数组
v0 = 0;
n = 200;
L = n;
%以下实示例每隔1m采样
x_L = 1:n; %采样点li
det_L = linspace(1,1,n);%rand(1,n);%
alpha = linspace(-pi/6,pi/6,n);%rand(1,n);%
beta = linspace(0,0,n);%rand(1,n);%
miu = linspace(0.2,0.2,n);%rand(1,n);%
%曲率改大，模拟直道路
rho = linspace(10000,10000,n);%rand(1,n);%
r = linspace(10000,10000,n);%rand(1,n);%
vw = 0;
M = 80;
g = 9.81;
K = 1;
W = 1500;
CP = 300;
vmax = 50;
vlimit = rand(1,n);
V0 = vmax*rand(1,n);
for i = 1:n
vlimit(i) = vmax;%min(vmax, sqrt(miu(i)*g*r(i)));
end
options=optimoptions(@fmincon,'Algorithm','sqp','MaxFunEvals',100000,'MaxIter',10000,'GradObj', 'on');
%优化算法：'active-set' 'interior-point' 'sqp' 'trust-region-reflective'
%'MaxFunEvals',100000 最大优化迭代次数100000
%'GradObj', 'on',开启梯度函数
[outcome,fval] = fmincon('func',V0,[],[],[],[],zeros(1,n),vlimit,'nonlcon',options);
%outcome为最终速度序列，fval为目标函数最小值
subplot(2, 2, 1);
plot([0,x_L], [v0,outcome])%画图v-x
axis([0 max(x_L) 0 max(outcome)]);%调整图纸坐标轴范围
xlabel('x_L/m');
ylabel('v/m*s-1');
title('Course cross section');
grid on;
P = 1:n;
for i=1:n
if i==1;
avgv = outcome(i)/2;
P(i) = M*(outcome(i).^2)/2/det_L(i)+K*((avgv+vw*cos(beta(i))).^2)+M*g*sin(alpha(i))+ (M*g*cos(alpha(i))+avgv.^2*M/rho(i))*miu(i);
else
avgv = (outcome(i)+outcome(i-1))/2;
P(i) = M*(outcome(i).^2-outcome(i-1).^2)/2/det_L(i)+K*((avgv+vw*cos(beta(i))).^2)+M*g*sin(alpha(i))+ (M*g*cos(alpha(i))+avgv.^2*M/rho(i))*miu(i);
end
end
subplot(2, 2, 2);
plot(x_L, P, 'o')%画图P-x
axis([0 max(x_L) 0 max(P)]);%调整图纸坐标轴范围
xlabel('x_L/m');
ylabel('P/W');
title('P---x_L');
grid on;
x = linspace(0,0,n);
height = linspace(0,0,n);
x(1) = 0;
height(1) = 0;
for i=2:n
x(i) = x(i-1) + det_L(i)*cos(alpha(i));
height(i) = height(i-1) + det_L(i)*sin(alpha(i));
end
subplot(2, 2, 3);
plot(x, height)%画图P-x
xlabel('x/m');
ylabel('height/m');
title('Course cross section');
grid on;
disp(fval)%输出最小时间