Observer-based adaptive fuzzy backstepping dynamic surface control design and stability analysis for MIMO stochastic nonlinear systems

Composite Adaptive Fuzzy Output Feedback Dynamic Surface Control Design for Uncertain Nonlinear Stochastic Systems with Input Quantization

“…h Remark 1 Note that from (62), we can only conclude that the state observer errors and tracking error satisfy that E e k k ð Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2M=ck min ðPÞ p and E S 1 j j ð Þ ffiffiffiffiffiffiffiffiffiffiffi ffi 2M=c p , we cannot conclude that the state observer errors and tracking errors asymptotically converge to zero. However, according to the authors in [8][9][10][11][12][13][14][15][16][17][18][19][20][21], we can make both the state observer errors and tracking errors to be small by increasing the design parameters c i and c i , or decreasing r i (i = 1, …, n).…”

“…However, the aforementioned control approaches are developed based on the assumption that the states of controlled systems are measured directly. The authors in [8][9][10][11] investigated the adaptive fuzzy and neural network backstepping control design methods for SISO, MIMO nonlinear systems, or large-scale stochastic nonlinear systems with immeasurable states. Although the adaptive fuzzy or NN backstepping stochastic nonlinear control has achieved a great progress, the existing results do not consider the problem of ''explosion of complexity.''…”

“…Although the adaptive fuzzy or NN backstepping stochastic nonlinear control has achieved a great progress, the existing results do not consider the problem of ''explosion of complexity.'' It should be mentioned that because of the employment of the backstepping design technique, the previous control design methods in [2][3][4][5][6][7][8][9][10][11] inevitably suffer from the problem of ''explosion of complexity,'' which is caused by repeating differentiations of some nonlinear functions, i.e., the virtual controllers designed at each step with the conventional backstepping technique. As a result, the complexity of a controller drastically grows as the order of the system increases.…”

“…(2) By designing a serial-parallel estimation model, the prediction errors between controlled stochastic nonlinear system model and serial-parallel estimation model have been incorporated into the control design scheme, and the proposed control scheme can achieve good control and tracking performances. (3) By using the new DSC technique, the proposed fuzzy adaptive control approach can overcome the defect of ''explosion of complexity'' existed in the references [2][3][4][5][6][7][8][9][10][11], thus the computational burden of the control algorithm can be reduced greatly. In addition, the DSC technique design in this paper uses two kinds of first-order filters instead of a first-order filter in [12][13][14]24].…”

Chaos RBF dynamics surface control of brushless DC motor with time delay based on tangent barrier Lyapunov function

“…Using the high-gain observer, an adaptive fuzzy backstepping output feedback control approach is developed for a class of multiple-input and multipleoutput (MIMO) nonlinear systems with time delays and immeasurable states [22]. For a class of MIMO stochastic nonlinear systems with immeasurable states, an adaptive fuzzy backstepping output feedback DSC approach is presented [23].…”