Event triggered control using ode45

I have to solve ODE given by:

dy/dt= y- (|y|^0.5)*signum(y).

And T1=2; is some given constant.

Where event points are generated by

s_(k+1)={ t >=t and t<T1_k: y(t)=e^-(t_k)}

where t_k= s_k+ r_k, r_k is the delay term . And at t=t_k, y(t) should update the initial condition as

y(t_k)=y((t_k)^)+ 0.5*|y(s_k)|/(1+0.5*)).

And for t>=T1 we should just solve the given ODE and there is event condition for t>=T1.

And we should plot t vs y(t) for 4 seconds.

Answer 1

[Walter Roberson]

Proceed as described in https://www.mathworks.com/matlabcentral/answers/2169908-while-in-ode45#answer_1552013

%assuming r_k is a row vector of delay intervals.
tspan = cumsum([0, r_k]).';
if tspan(end) == T1; tspan(end) = []; end
tspan = [tspan, [tspan(2:end); T1]];

and then run the for loop. Within the for loop, adjust the boundary condition after each ode45() call.

[Arnab]

Thank you