Using ode15s as a function of parameters in order to solve them with fsolve

Hello,

I am stuck with the following problem, if you could help it will be great.

I am trying to realise some kind of shooting method.

So I have a system of ode, whatever it is (contained in sysode), and I want to integrate it from left to right from t_0 to t_m and from right to left from t_end to t_m.

I know initial conditions at t_0, but not in t_end. Then i want to integrate first at left and then match the integration which starts from t_end, to obtain the initial condition at t_end.

So in my mind i would use a command like

 F0=lambda_1
u0=lambda_2
A0=lambda_3
B0=lambda_4
A10=lambda_5
B10=lambda_6
tspan = [5 1.6];
y0 = [F0 u0 A0 A10 B0 B10];
H10 = 0;
opts = odeset('RelTol', 1e-5, 'AbsTol', 1e-8,'Stats','on')
[t,y] = ode15s(@(t,y) sysedo(t,y,b0,b1,b2,b3), tspan, y0, opts);
lambda=fsolve(y(end,:)-yts(:,1),lambda_0)

where yts is given by the first integration from t_0 to t_m, and lambda_0 will be a vector for the initial guess.

So i want to use ode15s inside fsolve as a function of the lambda_i, to obtain them in the end, but i don't know how to do it.

Can you help me with this problem ?

Thank you for help.

Have a good day.