需要把J的输出改为三个维度的u的绝对值积分

为了将目标函数 \( J \) 改为三个维度的控制输入 \( u \) 的绝对值积分，你需要修改 `mlocpContinuous` 和 `mlocpEndpoint` 函数中的相应部分。具体步骤如下：

1. **修改 `mlocpContinuous` 函数**：在计算 `phaseout.integrand` 时，使用 \( u \) 的绝对值之和而不是平方和。
2. **修改 `mlocpEndpoint` 函数**：保持目标函数的形式不变，但确保它正确地处理新的积分形式。

以下是修改后的代码：

### 修改 `mlocpContinuous` 函数

function phaseout = mlocpContinuous(input)
    g = input.auxdata.g;
    t = input.phase.time;
    
    x = input.phase.state(:,1:3);
    v = input.phase.state(:,4:6);
    u = input.phase.control;
    
    dx = v;
    dv = u - [0, 0, 1.6];
    
    % 计算新的积分项，即三个维度的 u 的绝对值之和
    phaseout.dynamics = [dx, dv];
    phaseout.integrand = sum(abs(u), 2);
end

### 修改 `mlocpEndpoint` 函数

function output = mlocpEndpoint(input)
    J = input.phase.integral;
    % 目标函数仍然是 J 的总和
    output.objective = sum(J);
end

### 完整的修改后代码

% 初始参数设置
t0min = 0;
t0max = 0;
tfmin = 0;
tfmax = 30;

% 初始状态向量，包含位置和速度
h0 = [100, -200, 400, 0, 0, -10];

% 最终状态向量，包含位置和速度
hf = [0, 0, 0, 0, 0, 0];

% 状态变量的下限和上限
hmin = [-250, -250, 0, -50, -50, -50];
hmax = [450, 450, 450, 50, 50, 50];

% 控制变量的下限和上限
umin = [-3, -3, 0];
umax = [3, 3, 3];

% 重力加速度向量
setup.auxdata.g = [0, 0, 1.6];

% 边界条件设置
setup.bounds.phase.initialstate.lower = h0;
setup.bounds.phase.initialstate.upper = h0;
setup.bounds.phase.state.lower = hmin;
setup.bounds.phase.state.upper = hmax;
setup.bounds.phase.finalstate.lower = hf;
setup.bounds.phase.finalstate.upper = hf;
setup.bounds.phase.control.lower = umin;
setup.bounds.phase.control.upper = umax;
setup.bounds.phase.integral.lower = -100;
setup.bounds.phase.integral.upper = 100;
setup.bounds.phase.initialtime.lower = t0min;
setup.bounds.phase.initialtime.upper = t0max;
setup.bounds.phase.finaltime.lower = tfmin;
setup.bounds.phase.finaltime.upper = tfmax;

% 初值猜测
h_guess = [h0; hf];
u_guess = [umin; umin];
t_guess = [t0min; 5];
setup.guess.phase.state = h_guess;
setup.guess.phase.control = u_guess;
setup.guess.phase.time = t_guess;
setup.guess.phase.integral = 10;

% 设置求解器参数
setup.name = 'Moon-Lander-OCP';
setup.functions.continuous = @mlocpContinuous;
setup.functions.endpoint = @mlocpEndpoint;
setup.nlp.solver = 'snopt';
setup.derivatives.supplier = 'sparseCD';
setup.derivatives.derivativelevel = 'second';
setup.mesh.method = 'hp1';
setup.mesh.tolerance = 1e-4;
setup.mesh.maxiteration = 45;
setup.mesh.colpointsmax = 6;
setup.mesh.colpointsmin = 10;
setup.mesh.phase.fraction = 0.1*ones(1,10);
setup.mesh.phase.colpoints = 4*ones(1,10);
setup.method = 'RPMintegration';

% 求解最优控制问题
tic;
output = gpops2(setup);
toc;

% 结果可视化
solution = output.result.solution;
figure('Color',[1,1,1]);
plot(solution.phase.time, solution.phase.state(:,1),'-x','LineWidth',1.5);
xlabel('Time', 'FontWeight','bold');
ylabel('State', 'FontWeight','bold');
legend('Altitude')
set(gca,'FontName','Times New Roman', 'FontSize',15,'LineWidth',1.3);
print -dpng moonlander_state.png

figure('Color',[1,1,1]);
plot(solution.phase.time, solution.phase.state(:,2),'--','LineWidth',1.5);
xlabel('Time', 'FontWeight','bold');
ylabel('State', 'FontWeight','bold');
legend('Altitude')
set(gca,'FontName','Times New Roman', 'FontSize',15,'LineWidth',1.3);
print -dpng moonlander_state.png

figure('Color',[1,1,1]);
plot(solution.phase.time, solution.phase.control,'-o','LineWidth',1.5);
xlabel('Time', 'FontWeight','bold');
ylabel('Control', 'FontWeight','bold');
set(gca,'FontName','Times New Roman', 'FontSize',15,'LineWidth',1.3);
print -dpng moonlander_control.png

% 连续时间动态方程
function phaseout = mlocpContinuous(input)
    g = input.auxdata.g;
    t = input.phase.time;
    
    x = input.phase.state(:,1:3);
    v = input.phase.state(:,4:6);
    u = input.phase.control;
    
    dx = v;
    dv = u - [0, 0, 1.6];
    
    % 计算新的积分项，即三个维度的 u 的绝对值之和
    phaseout.dynamics = [dx, dv];
    phaseout.integrand = sum(abs(u), 2);
end

% 终值函数
function output = mlocpEndpoint(input)
    J = input.phase.integral;
    % 目标函数仍然是 J 的总和
    output.objective = sum(J);
end

通过这些修改，目标函数 \( J \) 将变为三个维度的控制输入 \( u \) 的绝对值积分。这将影响最优控制问题的求解结果。