To determine the regulator (28) for plant (25) with target vector (29) consider

Hamiltonian functionThe 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 [21].

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