Abstract
It has been known that there are many systems that have the same optimal feedback control law and the same solution of the Hamilton-Jacobe partial differential equation as ones that given optimal control systems have.
In this paper, if the situation stated above happens among systems, they are called to be “equivalent”, and when the optimal feedback control laws coincidence happens, they are called to be “subequivalent”. Thus the equivalent or subequivalent condition is thoroughly studied and sought.
For example, the necessary and sufficient conditions for equivalence between such two systems as,
x=f(x, u, t)J=∫tft0L(x, u, t)dt
and,
x=f*(x, u, t)J=∫tft0{L(x, u, t)+M(x, t)}dt
is obtained, and the sufficient condition for subequivalence between such two systems as,
x=f(x, u, t)J=∫tft0L(x, u, t)dt
and,
x=f*(x, u, t)J=∫tft0L*(x, u, t)dt
is also obtained.
By using these conditions, equivalent or subequivalent classes of optimal control systems can be generated. This paper demonstrates to be able to extend the well-known linear regulator system to a broder class of the system.
