To be expanded
Basically take a system with state evolving linearly as s(t+1) = a*s(t) + b1*u1(t) + b2*u2(t) and parameterize the actions ui(t) = ki*x(t) and perform gradient descent on the infinite time horizon cost on parameters (k1, k2) and see what the equilibria are.
The allowed parameters (k1,k2) such that |a+b1*k1+b2*k2|<1.
To be expanded
Basically take a system with state evolving linearly as
s(t+1) = a*s(t) + b1*u1(t) + b2*u2(t)and parameterize the actionsui(t) = ki*x(t)and perform gradient descent on the infinite time horizon cost on parameters (k1, k2) and see what the equilibria are.The allowed parameters (k1,k2) such that
|a+b1*k1+b2*k2|<1.