Hello, someboddy help me please with this optimal control problem of fixed end time and fixed end point using Pontryagin Minimum Principle
State equation
dx1(t)/dt = – (1/N)*d*x1(t)*x3(t) – u1*x1(t)
dx2(t)/dt = (1/N)*x1(t)*x3(t) – a*x2(t) – u2*x2(t)
dx3(t)/dt = a*x2(t) – b*x3(t) – u3*x3(t)
dx4(t)/dt = b*x3(t) – u4*x4(t)
with N=651
a=0.2
b=0.3
d=0.5
x1(0)=651 x1(T)=148
x2(0)=279 x2(T)=85
x3(0)=130 x3(T)=80
x4(0)=75 x4(T)=252
with T= 29
cost function minimize J = integral from 0 to 29 of 0.5*x1^2 + 0.5*x2^2 + 0.5*x3^2 + 0.5*x4^2 + 0.5*u1^2 + 0.5*u2^2 + 0.5*u3^2 + 0.5*u4^2

please help me with matlab coding
thank you very much
I appreciate for your helpHello, someboddy help me please with this optimal control problem of fixed end time and fixed end point using Pontryagin Minimum Principle
State equation
dx1(t)/dt = – (1/N)*d*x1(t)*x3(t) – u1*x1(t)
dx2(t)/dt = (1/N)*x1(t)*x3(t) – a*x2(t) – u2*x2(t)
dx3(t)/dt = a*x2(t) – b*x3(t) – u3*x3(t)
dx4(t)/dt = b*x3(t) – u4*x4(t)
with N=651
a=0.2
b=0.3
d=0.5
x1(0)=651 x1(T)=148
x2(0)=279 x2(T)=85
x3(0)=130 x3(T)=80
x4(0)=75 x4(T)=252
with T= 29
cost function minimize J = integral from 0 to 29 of 0.5*x1^2 + 0.5*x2^2 + 0.5*x3^2 + 0.5*x4^2 + 0.5*u1^2 + 0.5*u2^2 + 0.5*u3^2 + 0.5*u4^2

please help me with matlab coding
thank you very much
I appreciate for your help Hello, someboddy help me please with this optimal control problem of fixed end time and fixed end point using Pontryagin Minimum Principle
State equation
dx1(t)/dt = – (1/N)*d*x1(t)*x3(t) – u1*x1(t)
dx2(t)/dt = (1/N)*x1(t)*x3(t) – a*x2(t) – u2*x2(t)
dx3(t)/dt = a*x2(t) – b*x3(t) – u3*x3(t)
dx4(t)/dt = b*x3(t) – u4*x4(t)
with N=651
a=0.2
b=0.3
d=0.5
x1(0)=651 x1(T)=148
x2(0)=279 x2(T)=85
x3(0)=130 x3(T)=80
x4(0)=75 x4(T)=252
with T= 29
cost function minimize J = integral from 0 to 29 of 0.5*x1^2 + 0.5*x2^2 + 0.5*x3^2 + 0.5*x4^2 + 0.5*u1^2 + 0.5*u2^2 + 0.5*u3^2 + 0.5*u4^2

please help me with matlab coding
thank you very much
I appreciate for your help control, pontryagin MATLAB Answers — New Questions

​