A system of time optimal processes is dealt with in this paper. Differential equation of the sys-tem and admissible control
u are as follows:
x=Ax+uBx, u
min≤u≤
umax,
where function
x is a vector in n-dimensional Euclidian space,
A and
B are
n ×
n matrices, and it is a scalar function. The object in this optimal process is to have the trajectory reach a shell with a center at origin from an arbitrary point in
x-space. Using maximum principle and transversality condition, the admissible control
u, which is of bang-bang type, is obtained. Three syntheses are made in the differential equation of second order, that is, 1) parametric control for small damping, 2) parametric control for large damping, and 3) parametric control for restoring force. Uniqueness of the solution is not formed in the case of 2).
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