Adaptive fuzzy controller for a class of strict-feedback nonaffine nonlinear system

Abstract

A robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems with modeling uncertainties and external disturbances by using Backstepping approach. Fuzzy logic systems (FLS) are employed to approximate the unknown parts of the desired virtual controls, the key assumption is that the norms of the approximation errors are bounded, and the bounds are unknown. A robust control algorithm was introduced to efficiently compensate the approximation error and external disturbances. The tracking error is guaranteed to be uniformly ultimately bounded. Finally, by taking the complexity of FLS, tracking error and control oscillation as object functions, an elitist preserved genetic algorithm (GA) is employed to search for the optimal parameters. The simulation results illustrate the effectiveness of the proposed scheme.

Advanced backstepping control based on ADR for non-affine non-strict feedback nonlinear systems

“…where k 2 > 1 is a constant to be chosen. υ 1,2 is the state of TD defined in (18), avoiding the computation ofẋ 2d . Choose a Lyapunov function V 2 as follows:…”

“…Z n−2,2 , Z n−1,2 ,Z n,2 are the states of ESO defined in (17), which is used to estimate F n−2 , F n−1 , F n respectively in real time. υ n−1,2 is the state of TD defined in (18), avoiding the computation ofẋ nd , choose a Lyapunov function V n as follows:…”

“…The indirect adaptive fuzzy control laws for the chain integration system with nonaffine input proposed in [16,17] are composed of three terms: a linear term specifying the desired closed-loop dynamics, an adaptive fuzzy term used to approximately construct an ideal uncertainty compensator and a robustifying term applied to compensate for disturbances and approximation errors. The approach proposed in [16,17] is applied to the strict feedback nonlinear system with non-affine input [18] and a chaotic system with non-affine input [19]. More specifically, the basic idea in [16][17][18][19] that change the non-affine form into the affine form is adding and subtracting a linear term of control variable to non-affine input terms.…”

“…The approach proposed in [16,17] is applied to the strict feedback nonlinear system with non-affine input [18] and a chaotic system with non-affine input [19]. More specifically, the basic idea in [16][17][18][19] that change the non-affine form into the affine form is adding and subtracting a linear term of control variable to non-affine input terms. This basic idea is equivalent to the auto disturbance rejection controller (ADRC) design idea proposed in [20,21].…”