On the solution of time-optimal control problems in the presence of quadratic constraints

It is shown that the minimization of
\parallel k \parallel_{2}
with respect to λ results in a set of
m
equations which are linear in (
m - 1
) lambdas and nonlinear in the minimum time. These equations can also be obtained by satisfying the terminal conditions subject to the condition,
\lambda \cdot e_{d} = 1
.