Fuzzy Adaptive Quantized Control for a Class of Stochastic Nonlinear Uncertain Systems

Abstract

In this paper, a fuzzy adaptive approach for stochastic strict-feedback nonlinear systems with quantized input signal is developed. Compared with the existing research on quantized input problem, the existing works focus on quantized stabilization, while this paper considers the quantized tracking problem, which recovers stabilization as a special case. In addition, uncertain nonlinearity and the unknown stochastic disturbances are simultaneously considered in the quantized feedback control systems. By putting forward a new nonlinear decomposition of the quantized input, the relationship between the control signal and the quantized signal is established, as a result, the major technique difficulty arising from the piece-wise quantized input is overcome. Based on fuzzy logic systems' universal approximation capability, a novel fuzzy adaptive tracking controller is constructed via backstepping technique. The proposed controller guarantees that the tracking error converges to a neighborhood of the origin in the sense of probability and all the signals in the closed-loop system remain bounded in probability. Finally, an example illustrates the effectiveness of the proposed control approach.

Distributed Filtering for Fuzzy Time-Delay Systems With Packet Dropouts and Redundant Channels

“…In [20], a class of Takagi-Sugeno (T-S) fuzzy models, which is well recognized to be capable of approximating smooth nonlinear systems to any degree of accuracy, is adopted and has been shown to be quite helpful in facilitating the design of distributed filters. On the basics of T-S fuzzy modeling for nonlinear systems, and their recent advances, we refer readers to [21]- [24] for more details.…”

Fuzzy adaptive quantized output feedback tracking control for switched nonlinear systems with input quantization

“…Such systems are referred to as systems with quantized control input and the possible values of the input represent the levels of quantization. For example, hydraulic systems using on/off valves are systems with quantized input, digital control, hybrid systems, automotive powertrain systems, networked control systems (for information processing of networked systems, all signals must be quantized before data transmission) [3][4][5][41][42][43][44]. Therefore, the control design for quantized control systems is important.…”

“…In addition, Hayakawaa et al [3] and Zhou et al [4] required that the nonlinear functions included in the controlled systems are known or can be linearly parameterized. To overcome this difficult, Liu et al [5] proposed an adaptive fuzzy quantized control for a class of nonlinear stochastic systems, which don't need assume the controlled systems are completely known. Although, the results of the above have made some achievement, they all required the states of the controlled systems are measured directly, and did not consider the control design problem for uncertain switched nonlinear systems in strict-feedback form, in which the states are unavailable for measurement.…”

“…The authors in [6][7][8][9][10] studied the adaptive fuzzy or neural control design problems for non-strict-feedback nonlinear systems by combing backstepping technique. The characteristic of the non-strict-feedback nonlinear system is that system functions contain the whole state variables.…”

“…It should be mentioned that the adaptive fuzzy control design methods on uncertain nonlinear systems in strict-feedback form with input quantization has not been reported yet. And also, although many fuzzy or neural adaptive control design problems have been investigated for uncertain nonlinear systems by combining the adaptive backstepping design technique with fuzzy-logic-systems (FLSs) or neural-networks (NNs) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]45,46], these adaptive fuzzy or neural control schemes are all focused on the non-switched nonlinear systems.…”