Lecture 34 : Trajectory tracking control ( feed forward, computed torque and inverse dynamics approach)
Lyapunov's Notions of Stability:
Stability is the Characteristic of equilibrium of
Equilibrium is obtained by solving for x in
Equilibrium 0 is said to be stable if for each , for each there exists a such that
Figure 34.6(a)
Figure 34.6(b)
Equilibrium 0 is attractive if for each there is an such that
.
Equilibrium is said to be asymptotically stable if it is stable and attractive.
Figure 34.7(a)
Figure 34.7(b)
Derivative along Trajectories:
Definition: Let continuously differentiable with respect
to all of the arguments and let denote
the gradient of V with respect to x
(written as a row vector). Then the
function is defined by
but
And is called the
derivative of V along the
trajectories of.
Figure 34.8 Lyapunov function
Summary
Trajectory Tracking control : Feed forward and C T Control
Equilibrium is obtained by solving for x in
, for each 
there exists a 
such that
.
continuously differentiable with respect
to all of the arguments and let 
denote
the gradient of V with respect to x
(written as a row vector). Then the
function 
is defined by 
.
