Decentralized control of uncertain nonlinear stochastic systems based on DSC

Abstract

In this paper, the decentralized stabilization control approach based on the dynamic surface control (DSC) is proposed for a class of large-scale interconnected stochastic nonlinear systems. The proposed approach combined the existing dynamic surface control (DSC) with back-stepping technique. This approach can overcome the problem of "explosion of complexity" inherent in the back-stepping method. Thus, the proposed control approach is simpler than the traditional back-stepping control method for the large-scale interconnected stochastic nonlinear systems. The stability analysis shows that all the signals in the closedloop system are uniformly ultimately bounded (UUB). Finally, an example is provided to illustrate the effectiveness of the proposed control system.

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).…”

“…As a result, the complexity of a controller drastically grows as the order of the system increases. To solve the problem of the ''explosion of complexity'' inherent in adaptive backstepping design method, some adaptive fuzzy or NN dynamic surface control approaches have been extensively studied in [12][13][14] for several classes of uncertain stochastic nonlinear systems. However, the control approaches in [12][13][14] all can not solve the control problem for uncertain stochastic nonlinear systems with input quantization.…”

“…(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]. Consequently, the restrictive assumption on the bounds of the derivative of virtual control functions being known is removed.…”

Adaptive NN control for a class of stochastic nonlinear systems with unmodeled dynamics using DSC technique

“…For example, in [30], by approximating the unknown nonlinear functions with radial basis function (RBF), the dynamic surface control technique was incorporated into the existing neural network based adaptive control design framework. In [31], the dynamic surface technique was incorporated into the decentralized control for a class of largescale interconnected stochastic nonlinear system. Tong [32] incorporated the dynamic surface control technique into the first adaptive fuzzy control scheme for a class of stochastic nonlinear strict-feedback systems.…”

Decentralized adaptive neural control of nonlinear systems with unknown time delays

“…For systems with high uncertainty, which cannot be modeled or repeatable, adaptive neural control approach has obtained further development with the help of neural network (NN) approximation (e.g., [1][2][3][4][5]). Especially, for a wide class of non-matching uncertain nonlinear systems, many prospective adaptive control methodologies were proposed based on the idea of backstepping design approach by fusion of fuzzy approximation (e.g., [6][7][8][9][10][11][12][13][14]), and NN approximation (e.g., [15][16][17][18][19][20][21][22][23][24][25][26]). However, these control methods suffer from either a problem of computational explosion or a problem of dimension curse, or both problems.…”