It follows from the standard NNAC result  that system (11) driven by control law (19) with (20) achieves practical asymptotic stability in the sense that [e.sub.q] and [e.sub.[sigma]] converge to small neighborhoods of zero determined by K and [epsilon]*.
The construction of the proposed NNAC follows the following steps: (1) to construct regression functions [[phi].sub.j](x) in (16), select three Gaussian functions to cover each universe of [OMEGA]x such that j = 1 to 729; (2) set the filtered error parameters [[lambda].sub.1] = [[lambda].sub.2] = 20 in (12); (3) set the lower bound [G.sub.0] = diag(50000,1000) and the control gain K = diag(20,20) for the control law in (19); (4) set the learning rate matrix [GAMMA] = diag(300,100) for the adaptive law in (20).
Tracking results by the PD control and the proposed NNAC are demonstrated in Figures 2 and 3, respectively, and comparisons of system errors are given in Figure 5, where no load is applied on the actuator in this case.
To investigate the adaptability of the proposed NNAC, a 2 kg load is added to the link at t = 15 s.
This paper has successfully applied a NNAC method to control SVSAs.