Adaptive Fuzzy Immune Sliding Mode Control for a Class of Uncertain Nonlinear Systems

Abstract

In this paper, a stable adaptive fuzzy immune sliding mode controller(AFISMC) for a class of nonlinear uncertain systems is investigated. The fuzzy system is applied to approximate the unknown nonlinear function of plant, and then the estimation value of nonlinear function is used to design the control variable, the immune feedback system is used as a compensator for the fuzzy sliding control. The proposed approach does not need a bound to be known, only requiring that it exists, and has not any assumption for initial condition. The approach is applied to an inverted pendulum system via significant disturbances. Analysis of simulations reveals that proposed method is robust in the presence of uncertainties and bounded external disturbances.

Leader-follower formation tracking for differential-drive wheeled mobile robots with uncertainties and disturbances based on immune fuzzy quasi-sliding mode control

“…The time-varying gains and parameters from the AIS also show that they are able to adapt to obtain the compensatory effect without exceed control efforts (Figs. 31,32,24,25,16). Consequently, small errors are obtained, as well as the SMC and formation control aims are achieved (Figs.…”

“…And the Table 2 outlines the control system course in comparison to immune regulation process [37,54,55]. The terms k h and k s can be variables based on the antigens amount (e.g., a linear/nonlinear function or an adaptive parameter), as in [24], [25] and [27]. In this work, they are considered as positive constants, as in [23] and [26].…”

“…disturbances adaptively. For this, we established that the antigens amount is the sliding surface σ * , as in [23][24][25][26][27], and total stimulation received by B cells for antibody generation corresponds to the sliding mode portion gain G AIS of the AIS-SMC controller. In this way, by Eqs.…”

“…It can also be seen, from concepts summarized in Table 2, that the nonlinear function f (•) plays an important role related to regulation of the stimulus received by B cells, since the reaction can be defined by the activation or containment of the effect of T s cells. In some works, f (•) is described by an exponential function based on antigen consistency as in [24,25,27,31,32,34]. A fuzzy inference system is also used as in [23,26,29,30,[32][33][34][35][36][37], which usually consider the total stimulation received by B cells and its variation with a time delay of immune response.…”

“…Among these works only the last one considers the sliding mode control, but the formation control is not treated. When considering the SMC, most researches propose control structures inspired on the adaptive humoral/feedback immunity model, applying to different systems and problems, as in [23][24][25][26][27]. But, these works do not consider DWMRs.…”