Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications

Abstract

A direct adaptive fuzzy control algorithm is developed for a class of uncertain SISO nonlinear systems. In this algorithm, it doesn't require to assume that the system states are measurable. Therefore, it is needed to design an observer to estimate the system states. Compared with the numerous alternative approaches with respect to the observer design, the main advantage of the developed algorithm is that on-line computation burden is alleviated. It is proven that the developed algorithm can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to a small neighborhood around zero. The simulation examples validate the feasibility of the developed algorithm.

Decentralized adaptive output feedback fuzzy controller for a class of large-scale nonlinear systems

“…Remark 2 Unlike such 1 and positive constant assumptions as in [6,14,15,18,23,31,32,[36][37][38]41], etc., the input gains considered herein have been relaxed to unknown nonlinear functions. Assumption 3 [30,[33][34][35]…”

“…In most involved situations where system states are unavailable, output feedback or observer-based control techniques have to be applied. Confronted with those cases, the authors in the papers [13][14][15] and [16][17][18][19][20] proposed diverse observer-based indirect and direct adaptive fuzzy or fuzzy-neural control algorithms for nonlinear systems, respectively. DAC designs, as a general, have need of more constraints on the input gain than IAC ones.…”

“…Apart from the well-known fact that the input gains keep away from zero for controllable systems, not infrequently are additional constraints required to ensure the stability, convergence, and robustness of the controlled systems. For example, the DAFCs proposed in [18,23] require the control gain to be little more than positive constants. In [1], the DAFC algorithm was developed with the help of two extra assumptions in which the input gain can be resolved into two parts, known and unknown.…”

“…Secondly, the stability analysis of the closed-loop interactive system and the implementation of the output feedback mechanism are tackled without recourse to both the famous SPR condition and the conventional HGO as in the present literature [13, 14, 17-22, 26, 39-41], etc., so that the aforementioned disadvantages consequent upon them can be completely shunned. Thirdly, the input gains of the large-scale systems under consideration are relaxed from such conservative positive constants or little more than 1 as in [6,14,15,18,23,31,32,[36][37][38]41], etc. to unknown nonlinear functions, and the same bound availability assumptions on the lumped uncertainties as in [11,13,17,19,20,23,26,33], etc.…”

Adaptive fuzzy output-feedback control of uncertain SISO nonlinear systems

“…The indirect adaptive output-feedback schemes using FLS or FNN were studied in [16][17][18]. The direct adaptive output-feedback control approaches using FLS or FNN were also given in [19][20][21]. The combined adaptive output-feedback control schemes are designed in [22,23].…”