75
Consider again the nonlinear system N
N: x(t) = f(x(t), u(t), w*(t))
y(t) = Hx(t)
e(t) = r*(t) y(t) (5-1)
Here r (t) and w (t) indicate a particular reference and disturbance out
of the class of signals r(t) and w(t).
Now assume that for a certain nominal reference r*(t) and a nominal
(anticipated) disturbance w*(t) tracking can be achieved. In
otherwords, assumption (A.l) holds for the nominal signals so that the
following solution for (5-1) exists
x (t) = f(x (t), U (t), w (t))
y*(t) Hx*(t) (5-2)
0 = r*(t) y*(t)
^ dp
where x (t) and (t) are nominal state and input trajectories which
are necessary for tracking. We shall not require x*(t) and *(t) to
satisfy a linear differential equation such as the one given in assump-
up dp
tion (A.2). Instead, it shall be assumed that both x (t) and u (t) can
be generated by external means so that they are readily available. In
practice, an exact generation of these signals may not always be
possible, however, discussion of this circumstance is deferred until a
later section on robustness.
In certain applications it may be desirable to change the reference
signal to a value other than r*(t). (One such application for the