Page 194 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

Adaptive Dynamic Surface Output Feedback Control of Pure-Feedback Systems 191

Figure 11.3 Performance comparison of linear ESO and finite-time ESO. (A) Observer
performance of LESO; (B) Observer performance of FTESO.

both the dead-zone and unknown dynamics, and thus help to retain better
control response.

11.6 CONCLUSION

In this chapter, a modified robust dynamic surface feedback control is
proposed for a class of pure-feedback systems with input dead-zone. A co-
ordinate transform with newly defined state variables is performed to re-
formulate the system as a canonical form, and then a finite-time ESO is
used to handle the unmeasurable system states and estimate the lumped
uncertainties including the unknown dead-zone non-linearity and system
non-linearities. TD is employed to replace first order filters in each step
of DSC designs to improve the convergence performance. It is shown that
all the signals in the closed-loop system are UUB. The proposed approach
is derived without using function approximators (e.g., NN or FLS). Thus,
the time-consuming online learning is avoided. Numerical simulations il-
lustrate the effectiveness of the proposed control.

REFERENCES
[1] S.S. Ge, C. Wang, Adaptive NN control of uncertain nonlinear pure-feedback systems,
Automatica 38 (4) (2002) 671–682.
[2] Dan Wang, Neural network-based adaptive dynamic surface control of uncertain non-
linear pure-feedback systems, International Journal of Robust and Nonlinear Control
21 (5) (2011) 527–541.