Hamiltonian (control Theory) - Notation and Problem Statement

Notation and Problem Statement

A control is to be chosen so as to minimize the objective function

$J(u)=\Psi(x(T))+\int^T_0 L(x,u,t) dt$

where is the system state, which evolves according to the state equations

$\dot{x}=f(x,u,t) \qquad x(0)=x_0 \quad t \in$

and the control must satisfy the constraints

$a \le u(t) \le b \quad t \in$

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