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jjliu2012

新虫 (小有名气)

应助: 0 (幼儿园)
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在线: 34小时
虫号: 1562041
注册: 2012-01-03
专业: 控制理论与方法

[求助] 【求助一个关于最优控制的matlab问题（新手，请大家多多帮助）

Sample Text
最速下降法求最优控制u的matlab算法，各位大侠能否把这个主循环补充一下，不知道怎么回事，运行不了。是附件里文献的例子2，在第7页，多谢
%%%%%%%%%%%%%%%%%%%%%%
for i = 1:max_iteration
% 1) start with assumed control u and move forward
[Tx,X] = ode45(@(t,x) stateEq(t,x,u,Tu), [t0 tf], ...
initx, options);
% 2) Move backward to get the trajectory of costates
x1 = X(:,1); x2 = X(:,2);
[Tp,P] = ode45(@(t,p) costateEq(t,p,u,Tu,x1,x2,Tx), ...
[tf t0], initp, options);
p1 = P(:,1);
% Important: costate is stored in reverse order. The dimension of
% costates may also different from dimension of states
% Use interploate to make sure x and p is aligned along the time axis
p1 = interp1(Tp,p1,Tx);
% Calculate deltaH with x1(t), x2(t), p1(t), p2(t)
dH = pH(x1,p1,Tx,u,Tu);
H_Norm = dH'*dH;

% Calculate the cost function
J(i,1) = tf*(((x1')*x1 + (x2')*x2)/length(Tx) + ...
0.1*(u*u')/length(Tu));
% if dH/du < epslon, exit
if H_Norm < eps
% Display final cost
J(i,1)
break;
else
% adjust control for next iteration
u_old = u;
u = AdjControl(dH,Tx,u_old,Tu,step);
end;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% State equations
function dx = stateEq(t,x,u,Tu)
dx = zeros(2,1);
u = interp1(Tu,u,t); % Interploate the control at time t
dx(1) = -2*(x(1) + 0.25) + (x(2) + 0.5)*exp(25*x(1)/(x(1)+2)) ...
- (x(1) + 0.25).*u;
dx(2) = 0.5 - x(2) -(x(2) + 0.5)*exp(25*x(1)/(x(1)+2));
%%%%%%%%%%%%%%%%%%%%%%%
% Costate equations
function dp = costateEq(t,p,u,Tu,x1,x2,xt)
dp = zeros(2,1);
x1 = interp1(xt,x1,t); % Interploate the state varialbes
x2 = interp1(xt,x2,t);
u = interp1(Tu,u,t); % Interploate the control
dp(1) = p(1).*(u + exp((25*x1)/(x1 + 2)).*((25*x1)/(x1 + 2)^2 - ...
25/(x1 + 2))*(x2 + 1/2) + 2) - ...
2*x1 - p(2).*exp((25*x1)/(x1 + 2))*((25*x1)/(x1 + 2)^2 - ...
25/(x1 + 2))*(x2 + 1/2);
dp(2) = p(2).*(exp((25*x1)/(x1 + 2)) + 1) - ...
p(1).*exp((25*x1)/(x1 + 2)) - 2*x2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Partial derivative of H with respect to u
function dH = pH(x1,p1,tx,u,Tu)
% interploate the control
u = interp1(Tu,u,tx);
R = 0.1;
dH = 2*R*u - p1.*(x1 + 0.25);
%%%%%%%%%%%%%%%%%%%%%%%%%
% Adjust the control
function u_new = AdjControl(pH,tx,u,tu,step)
% interploate dH/du
pH = interp1(tx,pH,tu);
u_new = u - step*pH;
%%%%%%%%%%%%%%%%

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