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conditions will allow the true state trajectory to asymptotically
converge to the trajectory which gives zero tracking error. These
stability conditions are easily checked using Liapunov's indirect
method. It is noted, however, that with Liapunov's approach, the
tracking error may only asymptotically converge to zero for a limited
range of initial states. Roughly speaking, this can be considered
equivalent to requiring that the disturbance and reference signals
remain small.
In Chapter Three, using the approach developed for the nonlinear
problem, we rederive the well known conditions imposed for a solution to
the linear servomechanism problem.
In Chapter Four, selection of locally stabilizing feedback based on
linearization techniques is discussed in detail. Due to the complexity
of the stability problem, the control law derived here is for time-
invariant systems which are acted upon by small reference and distur
bance signals. Simulations of a nonlinear system are provided which
verify the design technique. Also discussed in Chapter Four is the
interpretation of using optimal control techniques to arrive at the
feedback law required for the linear servomechanism problem. In a
nonlinear system, however, a certain degree of stability is often
desired. Consequently, in order to achieve this stability using optimal
control theory, a well known technique due to Anderson and Moore [16] is
presented.
In Chapter Five, we develop a controller designed to solve the
nonlinear servomechanism problem when a nominal input and state
trajectory are supplied as open-loop commands. Here essentially no new
theory is needed since the control problem can actually be treated using