# using control constraints in ode45

52 views (last 30 days)
Kyle Stanhouse on 15 Jan 2012
Commented: yosra welhazi on 9 Apr 2015
I need to use ode45 to solve a system of simultaneous differential equations that must meet a constraint on a function of a couple of its variables (this is part of a control system on which there is a control constraint). I can’t find any help documentation that provides for this situation so I assume that it can be done manually. This means that I need to check the value of an expression that is a function of a portion of the solution vector at every time and step, and if it exceeds a constraint, I’ll need to recalculate that particular time step of the numerical integral. Without understanding the nuances of the underlying computations in ode45 it’s hard to tell how I should do that. Anyone know how?
Could I just rewrite the new system after checking the condition and ode45 will handle it correctly?
For example:
%the original system
%epsilon is a constant and ms and bs are computed before the following
dydt(1) = y(2);
u = -(2*epsilon^2*ms'*bs*y(2)^2+y(4))/(2*epsilon^2*ms'*ms);
dydt(2) = u;
dydt(3) = 0;
dydt(4) = -4*epsilon^2*(bs'*bs*y(2)^3+ms'*bs*y(2)*(-(2*epsilon^2*ms'*bs*y(2)^2+y(4))/(2*epsilon^2*ms'*ms)))-y(3);
%check for violation of constraint
u=f(y(1),y(2),y(3)
If (u >= constant)
u=constant
% constraint is violated, solve new system with constraint
dydt(1) = y(2);
dydt(2) = u;
dydt(3) = 0;
dydt(4) = -4*epsilon^2*(bs'*bs*y(2)^3+ms'*bs*y(2)*(-
(2*epsilon^2*ms'*bs*y(2)^2+y(4))/(2*epsilon^2*ms'*ms)))-y(3);
end
Basically what I need to know is how to make ode45 reiterate a step and use a different set of equations. There must be someway to impose constraints like this, maybe I missed it in the help files….
My question is similar to what someone is trying to do here: ( http://www.mathworks.com/matlabcentral/answers/14164-using-saturated-inputs-in-ode45), they have implemented the constraint before the set of differential equations which I think is incorrect due to the fact that his control inputs should be a function of the current states, not the ones from the last state….
Thanks,
Kyle Stanhouse
yosra welhazi on 9 Apr 2015
Dear friend;
I have the same problem as you and when I simulate and plot my control inputs, they are not saturated , what can I do please

Matt Tearle on 16 Jan 2012
I must be missing something subtle. It looks like your equations are essentially
dydt(1) = y(2);
if (f(y(1),(2),y(3)) < constant)
dydt(2) = -(2*epsilon^2...
else
dydt(2) = constant;
end
dydt(3) = 0;
dydt(4) = -4*epsilon...
Can you explain what I'm missing?
yosra welhazi on 9 Apr 2015
Dear friend;
I have the same problem as you and when I simulate and plot my control inputs, they are not saturated , what can I do please ? please help me