To determine the regulator (28) for plant (25) with target vector (29) consider Hamiltonian function
The proposed approach formulates the Hamiltonian function
by incorporating both the design and control variables.
They also assume the Hamiltonian function
near </pc/> satisfies Moser's normal form and lies is a strictly convex singular subset </S0 of H-1(0).
In order to apply this mechanism on the Schwarzschild black hole, we first presented a Hamiltonian function
for a general spherically symmetric space-time and showed that the resulting Hamiltonian equations yield the conventional Schwarzschild metric.
The current value Hamiltonian function
is defined as
It is possible because the motion of a test particle in a rotating barred galaxy model is given by a Hamiltonian function
This principle converts systems (1) and (4) into a problem of minimizing pointwise Hamiltonian function
H, which is formed by allowing each of the adjoint variables to correspond to each of the state variables accordingly and combining the results with the objective functional .
The Hamiltonian function
, H(y), defined by H(y) = H(p, q) is a polynomial in the variables p and q.
According to the optimal control theory, the value of the Hamiltonian function
comprising the objective function and the constraints should be kept as constant along the time axis.
The corresponding Hamiltonian function
then takes the form
Construction of Hamiltonian Function
. With the consumption function Qc, in formula (5), when the final time is given, energy consumption can be converted into a Lagrange problem with constrained terminal state, which corresponded to Hamilton function, as formula (11).
If we introduce the Hamiltonian function
H(t) and the conjugate moment p(t) as defined below